Research ArticleRelational Research between Chinarsquos Marine SampT andEconomy Based on RPGRA Model

Kedong Yin Suyuan Li and Xuemei Li

School of Economics Ocean University of China Qingdao 266100 China

Correspondence should be addressed to Xuemei Li lixuemeiouceducn

Received 28 February 2016 Accepted 26 June 2016

Academic Editor Peide Liu

Copyright copy 2016 Kedong Yin et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

To make up the defect of the existing model an improved grey relational model based on radian perspective (RPGRA) is putforward According to the similarity of the relative change trend of time series translating traditional grey relational degree intoradian algorithmwithin different piecewise functions it greatly improves the accuracy and validity of the research results bymakingfull use of the poor information in time series Meanwhile the properties of the RPGRA were discussed The relationship betweenChinarsquos marine SampT and marine economy is researched using the new model so the validity and creditability of RPGRA areillustratedThe empirical results show thatmarine scientific and technological research projects marine scientific and technologicalpatents granted and research funds receipts of the marine scientific research institutions have greater relationship with GOP whichindicates that they have more impact on Chinarsquos marine economy

1 Introduction

Introduction of Grey Relational Degree Grey system theory(GST) [1] as well as fuzzy set theory [2] and rough set theory[3] is one of the most widely used theories to research onuncertain problems These theories are developing rapidlyin recent years Take fuzzy set theory as an example manyscholars contributed to its development [4ndash9] Comparedwith fuzzy set theory and rough set theory GST has moreadvantages in ldquosmall sample and poor informationrdquo fieldsand it can make more contribution to semi-complex uncer-tainty problems

Grey relational analysis (GRA) is part of grey sys-tem theory which is suitable for solving problems withcomplicated interrelationships between multiple factors andvariables This method has been widely used to solve theuncertainty problems under the discrete data and incompleteinformation GRA is proposed to measure the degree ofcorrelation between sequences by calculating their similarityor proximity It is also the basis of grey system analysismodeling prediction and decision-making Recently greyrelational theory tends to be mature and it has emerged asan effective model to measure the correlation degree AfterGRA was first put forward by Deng more and more research

on the GRA and its applications has been performed Thereare some traditional correlation degrees such as the originalDeng correlation degree [10] the absolute correlation degree[11] the relative correlation degree and the comprehensivecorrelation degree [12] At the same time various improve-ments in correlation degree and its extension are cropping upsuch as Trsquos correlation degree [13] slope correlation [14] Brsquoscorrelation degree [15] Crsquos correlation degree [16] the generalcorrelation degree and many other new correlation degreemodels [17ndash22]

Recently grey relational degree model is applied to moreand wider fields such as three-dimensional space and paneldata model and it is also greatly improved For examplea multidimensional correlation degree which extended greyabsolute correlation degree based on matrix is proposed[23] an enhanced grey clustering analysis method basedon accumulation sequences using grey relational analysis(AGRA) is put forward [24] and a three-dimensional greyinterval relational degree model based on time index andscheme is established [25] And grey relational analysis iscombined with the Dumpster-Shafer theory of evidence [26]At the same time many scholars have improved GRA modelfrom different perspectives Seyed Hamid used the analyticnetwork process (ANP) to deal with the interdependencies

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 3401387 8 pageshttpdxdoiorg10115520163401387

2 Mathematical Problems in Engineering

among the criteria and modified the traditional grey rela-tional analysis (GRA) to better address the uncertaintiesinherent in supplier selection decisions [27] Wu et al intro-duced the fractional order grey relational degree to analyzethe relationship between sci-tech input and the economicgrowth of ChinaThey defined fractional order grey relationalanalysis (FGRA) based on a fractional order difference oper-ator and discussed the effect of different orders on grey rela-tional analysis [28]Wu et al proposed a grey relational analy-sismodel of scientific research ability onmusic based onAHPIt selected out dominant indicators and recessive indicators toevaluate software features and hardware features [28] Guo etal developed a new method based on the traditional GRAmethod to overcome its limitation In this sense they used adifferent distance between two intuitionistic fuzzy numbers[29] Li et al proposed a new GCRA model and put for-ward grey accumulation generation relational analysis modelbased on grey exponential law (AGRA) for nonequidistanceunequal-length (NDUL) sequences as research is requiredon nonequidistance unequal-length sequences [30ndash32] Liet al proposed an effectiveness evaluation method which isbased on the combination of the improved grey relationaldegree and the analytic hierarchy process (AHP) aiming atthe shortcoming that the calculation of the grey relationalcoefficient is influenced by the number of schemes anddistinguishing coefficients which causes inconsistency of theevaluation results in the traditional grey relational degree[33] Huang et al proposed the methodology of improvedGRA to solve the problems that existed in model validationbased on current GRA methods in view of the similarity andnearness between the simulations and flight-test time series(time-varying data) and it is proved that the improved modelsatisfies the four grey relational axioms [34] And there areother modified GRA models and their applications [35ndash40]

In conclusion many scholars have made contributionto the development of grey relational degree and theselectures deepen the improvement of GRA and GST at thesame time they also promote the research on uncertainproblems However these GRA models are mostly basedon the definition of distance slope and area They do notbreak away from the limitations and research it from anotherperspective which may cause disadvantages to research onsome complex problems

Introduction of Chinarsquos Marine SampT and Economy Marineeconomy refers to the development utilization and pro-tection of the marine industry activities It is an essentialnational development strategy to promote marine economyand build China into a maritime power In recent yearsChinarsquos marine economy has been developing rapidly Asmarine development report of China (2015) says gross oceanproduct (GOP) in 2015 is 6467 billion yuan which has anincrease of 7 over the previous year accounting for 96of gross domestic product (GDP)

Marine science and technology included marine scienceand marine technology Marine science is a science thatstudies various natural phenomena and processes in the seaand their changing regularity including physical oceanog-raphy biological oceanography marine geology and marine

chemistry Marine technology refers to the accumulatedexperience skills and equipment used in the marine devel-opment activities including marine engineering technologymarine biotechnology seabed mineral resources explorationtechnology water resources development by technologymarine environment protection technology marine observa-tion technology marine forecast prediction technology andocean information technology It can be said that marinescience and technology are the integration of traditional andmodern high-tech in the marine field

With the development of science and technology marinescience and technology play a more and more important roleinmarine economyMany scholars havemade research on theintrinsic relevance and interaction and they have confirmedthat marine science and technology play an important rolein promoting the development of marine economy Qiaoand Zhu used the C-D production function developmentmodel carried out empirical study on coastal area paneldata of years 2000ndash2008 and finally concluded the followingthe government input to ocean science and technology hasthe remarkable positive effect on marine economic growth[41] Dai et al used Stochastic Frontier Analysis (SFA) tomeasure the total factor productivity (TFP) index of marineSampT and Exploratory Spatial Data Analysis (ESDA) andSpatial Panel Econometric Models were applied to identifythe temporal and spatial distribution pattern and influencingfactors from 2006 to 2011 [42] Zhai and Business usedmarine economy double logarithmic production functionmodel for Chinarsquos coastal marine economy with panel dataeconometric analysis showed that the elasticity of marinecapital marine science and technology and marine labor ispositive [43] Zhang et al designed coupling parameter withcoupled degree and coupled coordination degree to build themodel of marine industrial aggregation and marine scienceand technology talents aggregation and put forward somemeasures of the collaborative development of two systemsbased on their current collaborative development situation[44] Liu et al calculated the marine science and technologytransfer rate of our country in the period 2000ndash2012 basedon the different scopes of the connotations and exploredthe appropriate method to calculate the marine science andtechnology transfer rate which is suitable for the currentdevelopment situation in the oceanic field in China [45]

Research Motivation Quantitative analysis of the relationshipbetween marine SampT and economy has great strategic sig-nificance to promote marine economy General quantitativeanalysis methods need adequate data but due to the lagof marine economy research in China relative data cannotmeet the requirements Fortunately grey relational analy-sis is effectively used in this field because it is applicablewhether the samples are enough or regular However onthe other hand GRA is not perfect and there is space forfurther development For example some models do not havethe properties of parallelism isotonicity uniqueness andsymmetry Even though some improvements have alreadybeen done by scholars real innovation is hard to see becausethey are still based on the definition of distance slope andarea Under these backgrounds a new model called grey

Mathematical Problems in Engineering 3

relational analysis based on radian perspective (RPGRA) isproposed in this paper This new model can effectively usethe poor information in time series and can improve theaccuracy and validity of the research results RPGRA usespiecewise linear representation (PLR) to translate traditionalgrey relational degree into radian algorithm within differentpiecewise functions What is more RPGRA has the prop-erties of normativity uniqueness and parallelism and canexpand some existing models

RPGRA translates traditional grey relational degree intoradian algorithm by using PLR a method to analyze thenonlinear system by analyzing the nonlinear characteristicsas a piecewise linear approximation The nonlinear curve isreplaced by a straight line segment according to the differentsection Zhang et al proposed a measurement that the timeseries are represented approximately with a sequence of theincluded angles between a pair of neighboring line segments[46]Ding et al proposed a radian-distancewhich can reservesegment trend information when compared with the angle-distance [47] In a word RPGRA is put forward on thebase of the algorithm of radian-distance and traditional greyrelational degree and it is applied to analyze the relationshipbetween Chinarsquos marine SampT and economy

2 Establishment and Properties ofthe RPGRA Model

21 Establishment of the RPGRA Model The basic idea ofthe RPGRA model is to calculate the grey relational degreeaccording to the relative change trend of time series UsePLR to translate traditional grey relational degree into radianalgorithm within different piecewise functions Then applyradian-distance algorithm into grey relational analysis toestablish RPGRA model to calculate the grey relationaldegree

Step 1 (transforming the original time series) Time series isone kind of typical discrete sequences and it can be expressedin many ways using some methods In this paper time serieswill be expressed as the form of piecewise function based onthe thought of PLR

Therefore the time series can usually be expressed as thefollowing formula

119883119898= (119909119898(1199051) 119909119898(1199052)) (119909

119898(119905119894minus1) 119909119898(119905119894))

(119909119898(119905119899minus1) 119909119898(119905119899))

(1)

where 119905119894denotes the observation time points 119898 denotes the

number of time series 119899 denotes the number of observingtime points in one series119909

119898(119905119894)denotes the observation value

of the 119898th time series at 119905119894 and (119909

119898(119905119894minus1) 119909119898(119905119894)) denotes

the line segment with the starting value and the final value(Figure 1)

Definition 1 Segmented radian (rad) is the radian of theangle (acute angle) between the straight line formed by twoadjacent points in time series and timeline Set rad is positiveif the angle is in the first quadrant and it is negative if the angleis in the fourth quadrant

y

x1(t1)

x1(t2)

x1(t3)

x1(t4)

x1(t5)

1205721(t2)

1205721(t3)

1205721(t4)

t1 t2 t3 t4 t5 t

Figure 1 PLR of time series

Definition 2 Before setting the radian time series one shouldset angle series Set the time series that can be expressed as119883119898= 120572119898(1199052) 120572119898(1199053) 120572

119898(119905119899minus1) and one defines it as

the corresponding angle series of the time series where 119899denotes the number of observing time points in one seriesand 120572119898119905119894denotes the counterclockwise angle between the line

segments (119909119898(119905119894minus1) 119909119898(119905119894)) and (119909

119898(119905119894) 119909119898(119905119894+1)) of the 119898th

time seriesSet

rad119898(119905119896) = arctan

119909119898(119905119896+1) minus 119909119898(119905119896)

Δ119905 (2)

And it is the radian time series

Step 2 (calculating the radian variation) Assume the intervalis [119901 119902] and then set the following formula as the variationfunction of the corresponding radian series from 119905

119896minus1to

119905119896

119910119898(119905119896) = rad

119898(119905119896) minus rad

119898(119905119896minus1) 119896 = 1 2 119899 minus 2 (3)

Step 3 It is calculating the grey relational coefficient

Definition 3 Assume that 1198830= 1199090(1199051) 1199090(1199052) 119909

0(119905119899)

and 119883119894= 119909

119894(1199051) 119909119894(1199052) 119909

119894(119905119899) (119894 = 1 2 119898) are

sequences in [119901 119902] respectively the following formula willbe defined to calculate the relational coefficient between thesetwo time series

1205850119894(119896) =

1

1 +10038161003816100381610038161199100 (119905119896) minus 119910119894 (119905119896)

1003816100381610038161003816

(4)

In order to effectively distinguish the grey relational coef-ficient generated by two different time series a comparativevariable is introduced into formula (4) which is the subtrac-tion variable |119910

0(119905119896) minus 119910119894(119905119896)| When the variation function of

two time series in eachΔ119905119896is similar the comparative variable

will tend to be 0 and then 1205850119894(119896) will tend to be 1 and vice

versa

4 Mathematical Problems in Engineering

Table 1 Original data added value of strategic marine emerging industries Unit 100 million yuanitem

Year Gross oceanproduct

Marine scientificresearch

institutions

Research funds receiptsof the marine scientificresearch institutions

Marine scientificand technologicalresearch projects

Marine scientifictheses published

Marine scientificand technologicalpatents granted

2006 215924 136 52893 6593 8492 3792007 256187 136 77394 7617 9104 3982008 29718 135 87697 8327 9485 4412009 322776 186 16016 12600 14451 12502010 395727 181 195508 13466 14296 14822011 45496 179 232219 14253 15547 20342012 500452 177 257723 15403 16713 27462013 54313 175 265564 16331 16284 3430Source from 2006sim2014 China Marine Statistical Yearbook

Definition 4 Assuming that 1198830= 1199090(1199051) 1199090(1199052) 119909

0(119905119899)

and 119883119894= 119909119894(1199051) 119909119894(1199052) 119909

119894(119905119899) are nonnegative sequen-

ces in [119901 119902] then

1205850119894=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) (5)

is named the grey relational degree of the RPGRA of 1198830and

119883119894 The greater 120585

0119894is the stronger the correlation between119883

0

and119883119894is

22 Property of RPGRA

Theorem 5 The properties of the model of RPGRA are asfollows

(1) |1205850119894| le 1

(2) Symmetry 1205850119894= 1205851198940

(3) Uniqueness and independence 1205850119894being unique for two

fixed sequences and not influenced by other sequences(4) Comparability

Proof (1) We can obtain rad119898(119905119896) isin (minus1205872 1205872) from

Definition 1 so minus1 lt 119910119898(119905119896) lt 1 hArr minus1 le 120585

0119894(119905119896) le 1

119894 = 1 2 119898 119896 = 2 3 119899 and [119901 119902] = ⋃119899minus2119896=1Δ119905119896hArr minus1 le

1205850119894= (1(119902 minus 119901))sum

119899

119896=2Δ119905119896sdot 1205850119894(119905119896) le 1

(2) According to the definitions of the grey relationalcoefficient and the grey relational degree of the RPGRAproperty (2) is obvious

(3) The grey relational coefficient and the grey relationaldegree of the RPGRA are only connected with the twosequences involved Once the sequences are determined theradians are determined Therefore 120585

0119894of certain sequences

are confirmed and are not affected by other sequences in thesystem

(4) This property is also correct due to property (3)

Theorem 6 Assume that there are two time series 1198830=

1199090(1199051) 1199090(1199052) 119909

0(119905119899) and 119883

119894= 119909

119894(1199051) 119909119894(1199052)

119909119894(119905119899) (119894 = 1 2 119898) and their grey relational degree is 120585

0119894

which satisfies |1205850119894| le 1 and 120585

0119894= 1 if and only if 119883

119894(119905119896) =

1198830(119905119896) + 119888 (119896 = 1 2 119899 119888 is a constant) then119883

0and119883

119894are

parallel that is the RPGRA model satisfies the normativity ofGST

Proof As |1205850119894| le 1 and 120585

0119894= 1 hArr 120585

0119894(119905119896) = 1 hArr 119910

0(119905119896) =

119910119894(119905119896) hArr rad

0(119905119896) minus rad

0(119905119896minus1) = rad

119894(119905119896) minus rad

119894(119905119896minus1) hArr

rad0(119905119896) minus rad

0(1199051) = rad

119894(119905119896) minus rad

119894(1199051) hArr rad

119894(119905119896) =

rad0(119905119896) minus rad

0(1199051) + rad

119894(1199051) hArr rad

119894(119905119896) = rad

0(119905119896) + 119888 hArr

119883119894(119905119896) = 119883

0(119905119896) + 119888 hArr 119883

0119883119894are parallel And 119888 = rad

119894(1199051) minus

rad0(1199051)

That is themodel of RPGRA satisfies the characteristic ofGRArsquos normativity So this property was proved

3 Application of the RPGRAModel for Relationship between ChinarsquosSampT and Economy

In recent years Chinarsquos marine economy has been developingrapidly and marine science and technology have attractedhigh attention from concerned governmental departmentsAccording to the China Marine Statistical Yearbook theinvestment of marine science and technology has beenincreasing with the years In 2013 the research funds receiptsof the marine scientific research institutions are 265563million yuan increasing 200 from 2008 The research ofChinarsquos SampT is still in the initial stage There are few dataand they are mainly from China Marine Statistical YearbookTaking the choice of variables by scholars in Introductionand the availability of data into comprehensive considera-tion five variables are selected to represent Chinarsquos SampT toresearch their correlation with marine economyThey are thenumber of marine scientific research institutions researchfunds receipts of the marine scientific research institutionsthe number of marine scientific and technological researchprojects the number of marine scientific theses publishedand the number ofmarine scientific and technological patentsgranted

31 Empirical Analysis on Correlation between Chinarsquos MarineSampT and Economy The original data of Chinarsquos marinescience and technology and gross ocean product (GOP) areshown in Table 1

Use formula (2) to get the radian time series as Table 2

Mathematical Problems in Engineering 5

Table 2 The corresponding radian series of the original time series

Items rad119898(119905119896)

rad119898(1199052) rad

119898(1199053) rad

119898(1199054) rad

119898(1199055) rad

119898(1199056) rad

119898(1199057) rad

119898(1199058)

Gross ocean product 15705 15706 15704 15707 15706 15706 15706Research institutions 00000 minus07854 15512 minus13734 minus11071 minus11071 minus11071

Research funds receipts 15708 15708 minus15708 15708 15708 15708 15708

Research projects 15698 15694 15706 15696 15695 15699 15697

Theses published 15692 15682 15706 minus15643 15700 15699 minus15685

Patents granted 15182 15475 15696 15665 15690 15694 15693

Table 3 Correlation coefficient of Chinarsquos marine science and technology

Items 120585(119905119896)

120585(1199051) 120585(119905

2) 120585(119905

3) 120585(119905

4) 120585(119905

5) 120585(119905

6)

Research institutions 05601 02997 02548 07897 09999 10000Research funds receipts 10000 02415 02415 10000 09999 10000Research projects 09996 09987 09988 09999 09995 09998Theses published 09990 09974 02418 02419 10000 02416Patents granted 09715 09783 09967 09975 09995 10000

Use formulas (3) and (4) to calculate 120585(119905119896) as Table 3

Use GOP as a basic sequence to calculate the correlationcoefficient of the five variables for Chinarsquos marine science andtechnology

According to formula (5) 1205850119894is calculated as follows

12058501=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 06507

12058502=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 07471

12058503=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 09994

12058504=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 06203

12058505=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 09906

(6)

The RPGRA degree between GOP and marine scientificand technological research projects is 09994 ranked firstthe degree of marine scientific and technological patentsgranted is 09906 ranked second the degree of researchfunds receipts of the marine scientific research institutions is07471 ranked third the degree of marine scientific researchinstitutions is 06507 ranked fourth and the degree ofmarinescientific theses published is 06203 ranked the lastThe valueof grey relational degree does not have practical significanceso the results of empirical analysis are only concerned withthe ranking and do not rigidly adhere to the value

32 Conclusion of Empirical Analysis According to theempirical results GOP and marine scientific and technologi-cal research projects have a greater correlation degreemarine

0

5000

10000

15000

20000

Research institutions Research funds receiptsResearch projects Theses publishedPatents granted Gross ocean product

2007 2008 2009 2010 2011 2012 201320060

10000

20000

30000

40000

50000

60000

Figure 2 Diagrams of Chinarsquos marine science and technologySource from 2006sim2014 China Marine Statistical Yearbook NoteOnly the gross ocean product uses the secondary coordinate

scientific and technological patents granted take the secondplace followed by research funds receipts of the marinescientific research institutions and the degree of marinescientific theses published is the last one The geometricfigure of four variables and GOP is shown in Figure 2 Fromthe trend we can see that GOP and research funds receiptspatents granted and research projects have the most similartrend and have the least similarity with research institutionswhich conform to the results of the empirical analysis andillustrate the effectiveness of RPGRA model

33 Comparative Analysis with Traditional Grey RelationalMethods In this part some traditional GRAmodels are alsoused to make comparative analysis We use RPGRA degreeDengrsquos correlation degree absolute correlation degree rel-ative correlation degree and comprehensive correlationdegree The calculation result and ranking result are shownas Tables 4 and 5

6 Mathematical Problems in Engineering

Table 4 Grey relational degrees of different methods

DegreeMethods

RPGRA degree Dengrsquos correlationdegree

Absolutecorrelation degree

Relative correlationdegree

Comprehensivecorrelation degree

ItemsResearch institutions 06507 08706 05009 06752 05880Research funds receipts 07471 07410 05299 07161 06230Research projects 09994 09687 06688 09562 08125Theses published 06203 09325 06485 08887 07686Patents granted 09906 06734 05347 06355 05851

Table 5 Ranking results of the grey relational degree of different methods

Ranking resultsMethods

RPGRA degree Dengrsquos correlationdegree

Absolutecorrelation degree

Relative correlationdegree

Comprehensivecorrelation degree

ItemsResearch institutions 4 3 5 4 4Research funds receipts 3 4 4 3 3Research projects 1 1 1 1 1Theses published 5 2 2 2 2Patents granted 2 5 3 5 5

By analysis and calculation the ranking results are variantin different methods But in general the top one of therankings is research funds receipts and the number ofresearch institutions ranks in the last two which indicatesRPGRA modelrsquos validity and creditability The empiricalresults show that marine scientific and technological researchprojects marine scientific and technological patents grantedand research funds receipts of the marine scientific researchinstitutions have a greater correlation with GOP whichindicates that they have more impact on Chinarsquos marineeconomy

Marine scientific and technological research projectsinclude five parts basic research applied research experi-mental development result application and scientific andtechnological service The number of marine researchprojects has increased 96 from 2008 and its developmentsituation is shown as Table 6 Research projects can promotethe investigation of marine research and resources theconstruction of marine ecological civilization and mainte-nance of maritime rights and interests And they can alsoenhance the national marine awareness improve the capacityof marine infrastructure and equipment and then serveand promote the development of marine economy In thenext phase of the work State Oceanic Administration willaccelerate the research projects about construction of marinepower marine integrated management maintenance of themarine rights and interests and marine legislation

Marine scientific and technological patents of theresearch include the number of patent applications acceptedand the number of patents granted and in this paper we usethe number of patents granted because only it can reflectthe patent of marine science and technology in our country

accurately and objectively Intellectual property is theproduct of the commodity economy and the development ofscience and technology As one of the forms of intellectualproperty protection patent plays an important role in thedevelopment of science and technology The number ofmarine scientific and technological patents has increased30 compared with last year and the number is still growingrapidly

Research funds receipts of the marine scientific researchinstitutions include routine fund and loans in the governmentinvestment in the capital construction scientific and techno-logical activities The investment scale and structure of sci-entific research funds are shown as Figure 3 We can see thatroutine fund accounts for the largest proportion while loansand government investment occupy little floorTherefore theinvestment scale and structure are not reasonable and theyare an important factor affecting the conversion of scienceand technology achievements Furthermore due to its highcorrelation with marine economy it may affect the furtherdevelopment of marine economy

4 Conclusions and Policy Recommendations

The RPGRA model was established based on the similarityof the relative change trend of time series and on a newradian perspective Then it is applied to analysis of Chinarsquosmarine SampT and marine economyThe grey relational degreebetween marine SampT index and economy reflects its positionand function in marine economy Index with greater corre-lation degree will have a greater impact on the developmentof the marine economy Relevant data of marine SampT ischosen to analyze the relationship between Chinarsquos marine

Mathematical Problems in Engineering 7

Table 6 Development situation of marine scientific and technological research projects Unit item

Year Number ofresearch projects Basic research Applied research Experimental

development Result application Scientific andtechnological service

2008 8327 2087 2623 1420 691 15062009 12600 2753 3338 2550 1074 28852010 13466 3104 3497 2838 1359 26682011 14253 3476 3696 2855 1453 27732012 15403 3756 3854 3569 1515 27092013 16331 4276 3735 3997 1516 2807

2009 2010 2011 2012 2013

Routine fundLoans

Government investment

0

20

40

60

80

100

()

Figure 3 Diagrams of investment scale and structure of scientificresearch funds

SampT and marine economy The empirical results show thatmarine scientific and technological research projects marinescientific and technological patents granted and researchfunds receipts of the marine scientific research institutionshave greater correlations with GOP which indicates that theyhave more impact on Chinarsquos marine economy

Therefore China needs to develop marine SampT espe-cially in research projects patents and research funds topromote marine economy and so as to make the economymore prosperous We need to further refine the NationalMarine EconomyDevelopment Plan to realize the sustainabledevelopment of marine economy in China and build Chinainto a maritime power

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The relevant researches done in this paper are supported bythe National Social Science FundMajor Projects (14ZDB151)General Financial Grant from theChina Postdoctoral ScienceFoundation (2015M580611) Qingdao Postdoctoral Appli-cation Research Project Funding (251) and FundamentalResearch Funds for the Central Universities (201613006201564031)

References

[1] J L Deng ldquoIntroduction to grey system theoryrdquoThe Journal ofGrey System vol 1 no 1 pp 1ndash24 1989

[2] L A Zadeh ldquoFuzzy algorithmsrdquo Information amp Control vol 12no 2 pp 94ndash102 1968

[3] Z Pawlak ldquoRough setsrdquo International Journal of Computer ampInformation Sciences vol 11 no 5 pp 341ndash356 1982

[4] P Liu L He and X Yu ldquoGeneralized hybrid aggregation opera-tors based on the 2-dimension uncertain linguistic informationfor multiple attribute group decision makingrdquo Group Decisionand Negotiation vol 25 no 1 pp 103ndash126 2016

[5] PD Liu Y Li and J Antucheviciene ldquoAmulti-criteria decision-making method based on intuitionistic trapezoidal fuzzy prior-itizedOWAoperatorrdquoTechnological and EconomicDevelopmentof Economy vol 22 no 3 pp 453ndash469 2016

[6] P Liu ldquoSome generalized dependent aggregation operators withintuitionistic linguistic numbers and their application to groupdecisionmakingrdquo Journal of Computer and System Sciences vol79 no 1 pp 131ndash143 2013

[7] P Liu and F Jin ldquoA multi-attribute group decision-makingmethod based on weighted geometric aggregation operators ofinterval-valued trapezoidal fuzzy numbersrdquoAppliedMathemat-ical Modelling vol 36 no 6 pp 2498ndash2509 2012

[8] P Liu X Zhang and F Jin ldquoA multi-attribute group decision-making method based on interval-valued trapezoidal fuzzynumbers hybrid harmonic averaging operatorsrdquo Journal ofIntelligent and Fuzzy Systems vol 23 no 5 pp 159ndash168 2012

[9] P Liu ldquoSome geometric aggregation operators based on intervalintuitionistic uncertain linguistic variables and their applicationto group decision makingrdquo Applied Mathematical Modellingvol 37 no 4 pp 2430ndash2444 2013

[10] J L Deng ldquoRelational space of grey theoryrdquo FuzzyMathematicsvol 4 no 2 pp 1ndash10 1985

[11] Z G Mei ldquoThe concept and computation method of greyabsolute correlation degreerdquo System Engineering no 05 pp 43ndash44 1992

[12] S F Liu Y G Dang Z G Fang et al Grey System Theory andApplication Science Press Beijing China 2012

[13] W X Tang ldquoThe concept and the computation method of Trsquoscorrelation degreerdquo Application of Statistics and Managementno 01 pp 34ndash37 1995

[14] Y G Dang ldquoResearch on grey relational analysis of sloperdquoSystem Sciences and Comprehensive Studies in Agriculture vol10 pp 331ndash337 1994

[15] Z L Wang and Q Y Wang ldquoSome properties of Grey B-relateddegreerdquo Journal of Hebei Mining and Civil Engineering Instituteno 3 pp 48ndash50 1992

[16] X H Zhao andQ YWang ldquoThe relational analysis of C-moderdquoJournal of Huazhong University of Science and Technology vol27 no 3 pp 75ndash77 1999

8 Mathematical Problems in Engineering

[17] H X Shi S F Liu Z G Fang et al ldquoThe model of greyperiodic incidence and their rehabilitationrdquo Chinese Journal ofManagement Science vol 3 pp 131ndash136 2008

[18] H Y Du H X Shi S F Liu et al ldquoStudy on the model ofgrey periodic incidence judged on sloperdquo Chinese Journal ofManagement Science no 01 pp 128ndash132 2010

[19] H J Xiong M Y Chen and T Qu ldquoSome extensions of greyrelational grade formulardquo Systems Engineering and Electronicsno 1 pp 8ndash10 2000

[20] Y G Dang S F Liu B Liu et al ldquoImprovement on degree ofgrey slope incidencerdquo Engineering Science vol 6 no 3 pp 41ndash44 2004

[21] Y G Sun and Y G Dang ldquoImproved model of slope greyrelational analysisrdquo Statistics and Decision no 15 pp 12ndash132007

[22] Y-G Sun and Y-G Dang ldquoImprovement on grey Trsquos correla-tion degreerdquo SystemEngineeringTheory and Practice vol 28 no4 pp 135ndash139 2008

[23] K Zhang and S-F Liu ldquoExtended clusters of grey incidencesfor panel data and its applicationrdquo System Engineering-Theory ampPractice vol 30 no 7 pp 1253ndash1259 2010

[24] X Li K W Hipel and Y Dang ldquoAn improved grey relationalanalysis approach for panel data clusteringrdquoExpert SystemswithApplications vol 42 no 23 pp 9105ndash9116 2015

[25] Y Wang X Shi J Sun and W Qian ldquoA grey interval relationaldegree-based dynamic multiattribute decision making methodand its application in investment decision makingrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 607016 6pages 2014

[26] Z Li G Wen and N Xie ldquoAn approach to fuzzy soft setsin decision making based on grey relational analysis andDempster-Shafer theory of evidence an application in medicaldiagnosisrdquo Artificial Intelligence in Medicine vol 64 no 3 pp161ndash171 2015

[27] S H Hashemi A Karimi and M Tavana ldquoAn integratedgreen supplier selection approachwith analytic network processand improved Grey relational analysisrdquo International Journal ofProduction Economics vol 159 pp 178ndash191 2015

[28] F L Wu F S Liu G L Yao et al ldquoFractional order greyrelational analysis and its applicationrdquo Scientia Iranica vol 22no 3 pp 1171ndash1178 2015

[29] X Guo Y Ni and Wangjia ldquoA grey relational analysis modelof scientific research ability on music based on AHP and itsrealizationrdquo International Journal of Signal Processing ImageProcessing amp Pattern Recognition vol 8 no 5 pp 211ndash222 2015

[30] G-W Wei ldquoGray relational analysis method for intuitionisticfuzzy multiple attribute decision makingrdquo Expert Systems withApplications vol 38 no 9 pp 11671ndash11677 2011

[31] X M Li Y G Dang and L Jin ldquoGrey trend analysis based ongrey relational degree with rate of change and its applicationrdquoChinese Journal of Management Science vol 23 no 9 pp 132ndash138 2015

[32] X Li Y Dang L Jin andWKang ldquoGCRAmodel for grey trendanalysis and its applicationrdquo Journal of Grey System vol 27 no1 pp 57ndash69 2015

[33] X M Li Y G Dang S Ding and J Zhang ldquoGrey accumula-tion generation relational analysis model for nonequidistanceunequal-length sequences and its applicationrdquo MathematicalProblems in Engineering vol 2014 Article ID 764857 8 pages2014

[34] G Q HuangW B Zhao and S H Xu ldquoA combinationmethodof improved grey relational degree and AHP for effectivenessevaluationrdquo in Proceedings of the 3rd International Conferenceon Mechatronics and Information Technology 2016

[35] X L Ning W U Ying-Xia Y U Tian-Peng et al ldquoResearchon comprehensive validation of simulation models based onimproved grey relational analysisrdquo Systems Engineering amp Elec-tronics vol 32 no 8 pp 1677ndash1679 2016

[36] N Xie Y Han and Z Li ldquoA novel approach to fuzzy soft sets indecision making based on grey relational analysis and MYCINcertainty factorrdquo International Journal of Computational Intelli-gence Systems vol 8 no 5 pp 959ndash976 2015

[37] W Wu and Y Peng ldquoExtension of grey relational analysis forfacilitating group consensus to oil spill emergency manage-mentrdquo Annals of Operations Research vol 238 no 1-2 pp 615ndash635 2016

[38] K Guo and Q Zhang ldquoDetecting communities in socialnetworks by local affinity propagation with grey relationalanalysisrdquo Grey Systems Theory and Application vol 5 no 1 pp31ndash40 2015

[39] X Liu and T Liu ldquoBlasting parameters optimization based ongrey relational analysisrdquo Gansu Metallurgy no 2 pp 1ndash3 2016

[40] NWang S X Zhang and J Cao ldquoApplication ofGrey relationalanalysis in evaluation of cross-fault deformation anomaly inter-ference factorsrdquo Journal of Seismological Research vol 38 no 1pp 90ndash98 2012

[41] J Qiao and J Zhu ldquoGovernment input to ocean science andtechnology and marine economic growth empirical studybased on panel datardquo Science and Technology ManagementResearch no 4 pp 37ndash40 2012

[42] B Dai G Jin and M Han ldquoAnalysis on temporal and spatialevolution of marine science and technology total factor pro-ductivity and its influencing factors in Chinese coastal areasrdquoGeographical Research vol 34 no 2 pp 328ndash340 2015

[43] R X Zhai and S O Business ldquoMarine science and technologyinvestment and marine economic growth an empirical studywith panel data in Chinarsquos coastal regionsrdquo Mathematics inPractice ampTheory no 4 pp 75ndash80 2014

[44] X X Zhang P F Zhang and X U Zi-Yi ldquoThe couplingevaluation model of Chinarsquos marine industrial aggregation andmarine science and technology talents aggregationrdquo Journal ofShandong University no 6 pp 118ndash128 2014

[45] D Liu X Li C Wang et al ldquoCalculating and forecasting ofmarine science and technology transfer raterdquoMarine Economyvol 5 no 2 pp 18ndash22 2015

[46] P Zhang X-R Li J-Y Zhang and Z-L Zhang ldquoIncludedangle distance of time series and similarity searchrdquo PatternRecognition and Artificial Intelligence vol 21 no 6 pp 763ndash7672008

[47] Y W Ding X H Yang A J Kavs et al ldquoSimilarity measure oftime series based on radian distancerdquo Journal of Electronics andInformation no 1 pp 122ndash128 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

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Stochastic AnalysisInternational Journal of

2 Mathematical Problems in Engineering

among the criteria and modified the traditional grey rela-tional analysis (GRA) to better address the uncertaintiesinherent in supplier selection decisions [27] Wu et al intro-duced the fractional order grey relational degree to analyzethe relationship between sci-tech input and the economicgrowth of ChinaThey defined fractional order grey relationalanalysis (FGRA) based on a fractional order difference oper-ator and discussed the effect of different orders on grey rela-tional analysis [28]Wu et al proposed a grey relational analy-sismodel of scientific research ability onmusic based onAHPIt selected out dominant indicators and recessive indicators toevaluate software features and hardware features [28] Guo etal developed a new method based on the traditional GRAmethod to overcome its limitation In this sense they used adifferent distance between two intuitionistic fuzzy numbers[29] Li et al proposed a new GCRA model and put for-ward grey accumulation generation relational analysis modelbased on grey exponential law (AGRA) for nonequidistanceunequal-length (NDUL) sequences as research is requiredon nonequidistance unequal-length sequences [30ndash32] Liet al proposed an effectiveness evaluation method which isbased on the combination of the improved grey relationaldegree and the analytic hierarchy process (AHP) aiming atthe shortcoming that the calculation of the grey relationalcoefficient is influenced by the number of schemes anddistinguishing coefficients which causes inconsistency of theevaluation results in the traditional grey relational degree[33] Huang et al proposed the methodology of improvedGRA to solve the problems that existed in model validationbased on current GRA methods in view of the similarity andnearness between the simulations and flight-test time series(time-varying data) and it is proved that the improved modelsatisfies the four grey relational axioms [34] And there areother modified GRA models and their applications [35ndash40]

In conclusion many scholars have made contributionto the development of grey relational degree and theselectures deepen the improvement of GRA and GST at thesame time they also promote the research on uncertainproblems However these GRA models are mostly basedon the definition of distance slope and area They do notbreak away from the limitations and research it from anotherperspective which may cause disadvantages to research onsome complex problems

Introduction of Chinarsquos Marine SampT and Economy Marineeconomy refers to the development utilization and pro-tection of the marine industry activities It is an essentialnational development strategy to promote marine economyand build China into a maritime power In recent yearsChinarsquos marine economy has been developing rapidly Asmarine development report of China (2015) says gross oceanproduct (GOP) in 2015 is 6467 billion yuan which has anincrease of 7 over the previous year accounting for 96of gross domestic product (GDP)

Marine science and technology included marine scienceand marine technology Marine science is a science thatstudies various natural phenomena and processes in the seaand their changing regularity including physical oceanog-raphy biological oceanography marine geology and marine

chemistry Marine technology refers to the accumulatedexperience skills and equipment used in the marine devel-opment activities including marine engineering technologymarine biotechnology seabed mineral resources explorationtechnology water resources development by technologymarine environment protection technology marine observa-tion technology marine forecast prediction technology andocean information technology It can be said that marinescience and technology are the integration of traditional andmodern high-tech in the marine field

With the development of science and technology marinescience and technology play a more and more important roleinmarine economyMany scholars havemade research on theintrinsic relevance and interaction and they have confirmedthat marine science and technology play an important rolein promoting the development of marine economy Qiaoand Zhu used the C-D production function developmentmodel carried out empirical study on coastal area paneldata of years 2000ndash2008 and finally concluded the followingthe government input to ocean science and technology hasthe remarkable positive effect on marine economic growth[41] Dai et al used Stochastic Frontier Analysis (SFA) tomeasure the total factor productivity (TFP) index of marineSampT and Exploratory Spatial Data Analysis (ESDA) andSpatial Panel Econometric Models were applied to identifythe temporal and spatial distribution pattern and influencingfactors from 2006 to 2011 [42] Zhai and Business usedmarine economy double logarithmic production functionmodel for Chinarsquos coastal marine economy with panel dataeconometric analysis showed that the elasticity of marinecapital marine science and technology and marine labor ispositive [43] Zhang et al designed coupling parameter withcoupled degree and coupled coordination degree to build themodel of marine industrial aggregation and marine scienceand technology talents aggregation and put forward somemeasures of the collaborative development of two systemsbased on their current collaborative development situation[44] Liu et al calculated the marine science and technologytransfer rate of our country in the period 2000ndash2012 basedon the different scopes of the connotations and exploredthe appropriate method to calculate the marine science andtechnology transfer rate which is suitable for the currentdevelopment situation in the oceanic field in China [45]

Research Motivation Quantitative analysis of the relationshipbetween marine SampT and economy has great strategic sig-nificance to promote marine economy General quantitativeanalysis methods need adequate data but due to the lagof marine economy research in China relative data cannotmeet the requirements Fortunately grey relational analy-sis is effectively used in this field because it is applicablewhether the samples are enough or regular However onthe other hand GRA is not perfect and there is space forfurther development For example some models do not havethe properties of parallelism isotonicity uniqueness andsymmetry Even though some improvements have alreadybeen done by scholars real innovation is hard to see becausethey are still based on the definition of distance slope andarea Under these backgrounds a new model called grey

Mathematical Problems in Engineering 3

relational analysis based on radian perspective (RPGRA) isproposed in this paper This new model can effectively usethe poor information in time series and can improve theaccuracy and validity of the research results RPGRA usespiecewise linear representation (PLR) to translate traditionalgrey relational degree into radian algorithm within differentpiecewise functions What is more RPGRA has the prop-erties of normativity uniqueness and parallelism and canexpand some existing models

RPGRA translates traditional grey relational degree intoradian algorithm by using PLR a method to analyze thenonlinear system by analyzing the nonlinear characteristicsas a piecewise linear approximation The nonlinear curve isreplaced by a straight line segment according to the differentsection Zhang et al proposed a measurement that the timeseries are represented approximately with a sequence of theincluded angles between a pair of neighboring line segments[46]Ding et al proposed a radian-distancewhich can reservesegment trend information when compared with the angle-distance [47] In a word RPGRA is put forward on thebase of the algorithm of radian-distance and traditional greyrelational degree and it is applied to analyze the relationshipbetween Chinarsquos marine SampT and economy

2 Establishment and Properties ofthe RPGRA Model

21 Establishment of the RPGRA Model The basic idea ofthe RPGRA model is to calculate the grey relational degreeaccording to the relative change trend of time series UsePLR to translate traditional grey relational degree into radianalgorithm within different piecewise functions Then applyradian-distance algorithm into grey relational analysis toestablish RPGRA model to calculate the grey relationaldegree

Step 1 (transforming the original time series) Time series isone kind of typical discrete sequences and it can be expressedin many ways using some methods In this paper time serieswill be expressed as the form of piecewise function based onthe thought of PLR

Therefore the time series can usually be expressed as thefollowing formula

119883119898= (119909119898(1199051) 119909119898(1199052)) (119909

119898(119905119894minus1) 119909119898(119905119894))

(119909119898(119905119899minus1) 119909119898(119905119899))

(1)

where 119905119894denotes the observation time points 119898 denotes the

number of time series 119899 denotes the number of observingtime points in one series119909

119898(119905119894)denotes the observation value

of the 119898th time series at 119905119894 and (119909

119898(119905119894minus1) 119909119898(119905119894)) denotes

the line segment with the starting value and the final value(Figure 1)

Definition 1 Segmented radian (rad) is the radian of theangle (acute angle) between the straight line formed by twoadjacent points in time series and timeline Set rad is positiveif the angle is in the first quadrant and it is negative if the angleis in the fourth quadrant

y

x1(t1)

x1(t2)

x1(t3)

x1(t4)

x1(t5)

1205721(t2)

1205721(t3)

1205721(t4)

t1 t2 t3 t4 t5 t

Figure 1 PLR of time series

Definition 2 Before setting the radian time series one shouldset angle series Set the time series that can be expressed as119883119898= 120572119898(1199052) 120572119898(1199053) 120572

119898(119905119899minus1) and one defines it as

the corresponding angle series of the time series where 119899denotes the number of observing time points in one seriesand 120572119898119905119894denotes the counterclockwise angle between the line

segments (119909119898(119905119894minus1) 119909119898(119905119894)) and (119909

119898(119905119894) 119909119898(119905119894+1)) of the 119898th

time seriesSet

rad119898(119905119896) = arctan

119909119898(119905119896+1) minus 119909119898(119905119896)

Δ119905 (2)

And it is the radian time series

Step 2 (calculating the radian variation) Assume the intervalis [119901 119902] and then set the following formula as the variationfunction of the corresponding radian series from 119905

119896minus1to

119905119896

119910119898(119905119896) = rad

119898(119905119896) minus rad

119898(119905119896minus1) 119896 = 1 2 119899 minus 2 (3)

Step 3 It is calculating the grey relational coefficient

Definition 3 Assume that 1198830= 1199090(1199051) 1199090(1199052) 119909

0(119905119899)

and 119883119894= 119909

119894(1199051) 119909119894(1199052) 119909

119894(119905119899) (119894 = 1 2 119898) are

sequences in [119901 119902] respectively the following formula willbe defined to calculate the relational coefficient between thesetwo time series

1205850119894(119896) =

1

1 +10038161003816100381610038161199100 (119905119896) minus 119910119894 (119905119896)

1003816100381610038161003816

(4)

In order to effectively distinguish the grey relational coef-ficient generated by two different time series a comparativevariable is introduced into formula (4) which is the subtrac-tion variable |119910

0(119905119896) minus 119910119894(119905119896)| When the variation function of

two time series in eachΔ119905119896is similar the comparative variable

will tend to be 0 and then 1205850119894(119896) will tend to be 1 and vice

versa

4 Mathematical Problems in Engineering

Table 1 Original data added value of strategic marine emerging industries Unit 100 million yuanitem

Year Gross oceanproduct

Marine scientificresearch

institutions

Research funds receiptsof the marine scientificresearch institutions

Marine scientificand technologicalresearch projects

Marine scientifictheses published

Marine scientificand technologicalpatents granted

2006 215924 136 52893 6593 8492 3792007 256187 136 77394 7617 9104 3982008 29718 135 87697 8327 9485 4412009 322776 186 16016 12600 14451 12502010 395727 181 195508 13466 14296 14822011 45496 179 232219 14253 15547 20342012 500452 177 257723 15403 16713 27462013 54313 175 265564 16331 16284 3430Source from 2006sim2014 China Marine Statistical Yearbook

Definition 4 Assuming that 1198830= 1199090(1199051) 1199090(1199052) 119909

0(119905119899)

and 119883119894= 119909119894(1199051) 119909119894(1199052) 119909

119894(119905119899) are nonnegative sequen-

ces in [119901 119902] then

1205850119894=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) (5)

is named the grey relational degree of the RPGRA of 1198830and

119883119894 The greater 120585

0119894is the stronger the correlation between119883

0

and119883119894is

22 Property of RPGRA

Theorem 5 The properties of the model of RPGRA are asfollows

(1) |1205850119894| le 1

(2) Symmetry 1205850119894= 1205851198940

(3) Uniqueness and independence 1205850119894being unique for two

fixed sequences and not influenced by other sequences(4) Comparability

Proof (1) We can obtain rad119898(119905119896) isin (minus1205872 1205872) from

Definition 1 so minus1 lt 119910119898(119905119896) lt 1 hArr minus1 le 120585

0119894(119905119896) le 1

119894 = 1 2 119898 119896 = 2 3 119899 and [119901 119902] = ⋃119899minus2119896=1Δ119905119896hArr minus1 le

1205850119894= (1(119902 minus 119901))sum

119899

119896=2Δ119905119896sdot 1205850119894(119905119896) le 1

(2) According to the definitions of the grey relationalcoefficient and the grey relational degree of the RPGRAproperty (2) is obvious

(3) The grey relational coefficient and the grey relationaldegree of the RPGRA are only connected with the twosequences involved Once the sequences are determined theradians are determined Therefore 120585

0119894of certain sequences

are confirmed and are not affected by other sequences in thesystem

(4) This property is also correct due to property (3)

Theorem 6 Assume that there are two time series 1198830=

1199090(1199051) 1199090(1199052) 119909

0(119905119899) and 119883

119894= 119909

119894(1199051) 119909119894(1199052)

119909119894(119905119899) (119894 = 1 2 119898) and their grey relational degree is 120585

0119894

which satisfies |1205850119894| le 1 and 120585

0119894= 1 if and only if 119883

119894(119905119896) =

1198830(119905119896) + 119888 (119896 = 1 2 119899 119888 is a constant) then119883

0and119883

119894are

parallel that is the RPGRA model satisfies the normativity ofGST

Proof As |1205850119894| le 1 and 120585

0119894= 1 hArr 120585

0119894(119905119896) = 1 hArr 119910

0(119905119896) =

119910119894(119905119896) hArr rad

0(119905119896) minus rad

0(119905119896minus1) = rad

119894(119905119896) minus rad

119894(119905119896minus1) hArr

rad0(119905119896) minus rad

0(1199051) = rad

119894(119905119896) minus rad

119894(1199051) hArr rad

119894(119905119896) =

rad0(119905119896) minus rad

0(1199051) + rad

119894(1199051) hArr rad

119894(119905119896) = rad

0(119905119896) + 119888 hArr

119883119894(119905119896) = 119883

0(119905119896) + 119888 hArr 119883

0119883119894are parallel And 119888 = rad

119894(1199051) minus

rad0(1199051)

That is themodel of RPGRA satisfies the characteristic ofGRArsquos normativity So this property was proved

3 Application of the RPGRAModel for Relationship between ChinarsquosSampT and Economy

In recent years Chinarsquos marine economy has been developingrapidly and marine science and technology have attractedhigh attention from concerned governmental departmentsAccording to the China Marine Statistical Yearbook theinvestment of marine science and technology has beenincreasing with the years In 2013 the research funds receiptsof the marine scientific research institutions are 265563million yuan increasing 200 from 2008 The research ofChinarsquos SampT is still in the initial stage There are few dataand they are mainly from China Marine Statistical YearbookTaking the choice of variables by scholars in Introductionand the availability of data into comprehensive considera-tion five variables are selected to represent Chinarsquos SampT toresearch their correlation with marine economyThey are thenumber of marine scientific research institutions researchfunds receipts of the marine scientific research institutionsthe number of marine scientific and technological researchprojects the number of marine scientific theses publishedand the number ofmarine scientific and technological patentsgranted

31 Empirical Analysis on Correlation between Chinarsquos MarineSampT and Economy The original data of Chinarsquos marinescience and technology and gross ocean product (GOP) areshown in Table 1

Use formula (2) to get the radian time series as Table 2

Mathematical Problems in Engineering 5

Table 2 The corresponding radian series of the original time series

Items rad119898(119905119896)

rad119898(1199052) rad

119898(1199053) rad

119898(1199054) rad

119898(1199055) rad

119898(1199056) rad

119898(1199057) rad

119898(1199058)

Gross ocean product 15705 15706 15704 15707 15706 15706 15706Research institutions 00000 minus07854 15512 minus13734 minus11071 minus11071 minus11071

Research funds receipts 15708 15708 minus15708 15708 15708 15708 15708

Research projects 15698 15694 15706 15696 15695 15699 15697

Theses published 15692 15682 15706 minus15643 15700 15699 minus15685

Patents granted 15182 15475 15696 15665 15690 15694 15693

Table 3 Correlation coefficient of Chinarsquos marine science and technology

Items 120585(119905119896)

120585(1199051) 120585(119905

2) 120585(119905

3) 120585(119905

4) 120585(119905

5) 120585(119905

6)

Research institutions 05601 02997 02548 07897 09999 10000Research funds receipts 10000 02415 02415 10000 09999 10000Research projects 09996 09987 09988 09999 09995 09998Theses published 09990 09974 02418 02419 10000 02416Patents granted 09715 09783 09967 09975 09995 10000

Use formulas (3) and (4) to calculate 120585(119905119896) as Table 3

Use GOP as a basic sequence to calculate the correlationcoefficient of the five variables for Chinarsquos marine science andtechnology

According to formula (5) 1205850119894is calculated as follows

12058501=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 06507

12058502=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 07471

12058503=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 09994

12058504=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 06203

12058505=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 09906

(6)

The RPGRA degree between GOP and marine scientificand technological research projects is 09994 ranked firstthe degree of marine scientific and technological patentsgranted is 09906 ranked second the degree of researchfunds receipts of the marine scientific research institutions is07471 ranked third the degree of marine scientific researchinstitutions is 06507 ranked fourth and the degree ofmarinescientific theses published is 06203 ranked the lastThe valueof grey relational degree does not have practical significanceso the results of empirical analysis are only concerned withthe ranking and do not rigidly adhere to the value

32 Conclusion of Empirical Analysis According to theempirical results GOP and marine scientific and technologi-cal research projects have a greater correlation degreemarine

0

5000

10000

15000

20000

Research institutions Research funds receiptsResearch projects Theses publishedPatents granted Gross ocean product

2007 2008 2009 2010 2011 2012 201320060

10000

20000

30000

40000

50000

60000

Figure 2 Diagrams of Chinarsquos marine science and technologySource from 2006sim2014 China Marine Statistical Yearbook NoteOnly the gross ocean product uses the secondary coordinate

scientific and technological patents granted take the secondplace followed by research funds receipts of the marinescientific research institutions and the degree of marinescientific theses published is the last one The geometricfigure of four variables and GOP is shown in Figure 2 Fromthe trend we can see that GOP and research funds receiptspatents granted and research projects have the most similartrend and have the least similarity with research institutionswhich conform to the results of the empirical analysis andillustrate the effectiveness of RPGRA model

33 Comparative Analysis with Traditional Grey RelationalMethods In this part some traditional GRAmodels are alsoused to make comparative analysis We use RPGRA degreeDengrsquos correlation degree absolute correlation degree rel-ative correlation degree and comprehensive correlationdegree The calculation result and ranking result are shownas Tables 4 and 5

6 Mathematical Problems in Engineering

Table 4 Grey relational degrees of different methods

DegreeMethods

RPGRA degree Dengrsquos correlationdegree

Absolutecorrelation degree

Relative correlationdegree

Comprehensivecorrelation degree

ItemsResearch institutions 06507 08706 05009 06752 05880Research funds receipts 07471 07410 05299 07161 06230Research projects 09994 09687 06688 09562 08125Theses published 06203 09325 06485 08887 07686Patents granted 09906 06734 05347 06355 05851

Table 5 Ranking results of the grey relational degree of different methods

Ranking resultsMethods

RPGRA degree Dengrsquos correlationdegree

Absolutecorrelation degree

Relative correlationdegree

Comprehensivecorrelation degree

ItemsResearch institutions 4 3 5 4 4Research funds receipts 3 4 4 3 3Research projects 1 1 1 1 1Theses published 5 2 2 2 2Patents granted 2 5 3 5 5

By analysis and calculation the ranking results are variantin different methods But in general the top one of therankings is research funds receipts and the number ofresearch institutions ranks in the last two which indicatesRPGRA modelrsquos validity and creditability The empiricalresults show that marine scientific and technological researchprojects marine scientific and technological patents grantedand research funds receipts of the marine scientific researchinstitutions have a greater correlation with GOP whichindicates that they have more impact on Chinarsquos marineeconomy

Marine scientific and technological research projectsinclude five parts basic research applied research experi-mental development result application and scientific andtechnological service The number of marine researchprojects has increased 96 from 2008 and its developmentsituation is shown as Table 6 Research projects can promotethe investigation of marine research and resources theconstruction of marine ecological civilization and mainte-nance of maritime rights and interests And they can alsoenhance the national marine awareness improve the capacityof marine infrastructure and equipment and then serveand promote the development of marine economy In thenext phase of the work State Oceanic Administration willaccelerate the research projects about construction of marinepower marine integrated management maintenance of themarine rights and interests and marine legislation

Marine scientific and technological patents of theresearch include the number of patent applications acceptedand the number of patents granted and in this paper we usethe number of patents granted because only it can reflectthe patent of marine science and technology in our country

accurately and objectively Intellectual property is theproduct of the commodity economy and the development ofscience and technology As one of the forms of intellectualproperty protection patent plays an important role in thedevelopment of science and technology The number ofmarine scientific and technological patents has increased30 compared with last year and the number is still growingrapidly

Research funds receipts of the marine scientific researchinstitutions include routine fund and loans in the governmentinvestment in the capital construction scientific and techno-logical activities The investment scale and structure of sci-entific research funds are shown as Figure 3 We can see thatroutine fund accounts for the largest proportion while loansand government investment occupy little floorTherefore theinvestment scale and structure are not reasonable and theyare an important factor affecting the conversion of scienceand technology achievements Furthermore due to its highcorrelation with marine economy it may affect the furtherdevelopment of marine economy

4 Conclusions and Policy Recommendations

The RPGRA model was established based on the similarityof the relative change trend of time series and on a newradian perspective Then it is applied to analysis of Chinarsquosmarine SampT and marine economyThe grey relational degreebetween marine SampT index and economy reflects its positionand function in marine economy Index with greater corre-lation degree will have a greater impact on the developmentof the marine economy Relevant data of marine SampT ischosen to analyze the relationship between Chinarsquos marine

Mathematical Problems in Engineering 7

Table 6 Development situation of marine scientific and technological research projects Unit item

Year Number ofresearch projects Basic research Applied research Experimental

development Result application Scientific andtechnological service

2008 8327 2087 2623 1420 691 15062009 12600 2753 3338 2550 1074 28852010 13466 3104 3497 2838 1359 26682011 14253 3476 3696 2855 1453 27732012 15403 3756 3854 3569 1515 27092013 16331 4276 3735 3997 1516 2807

2009 2010 2011 2012 2013

Routine fundLoans

Government investment

0

20

40

60

80

100

()

Figure 3 Diagrams of investment scale and structure of scientificresearch funds

SampT and marine economy The empirical results show thatmarine scientific and technological research projects marinescientific and technological patents granted and researchfunds receipts of the marine scientific research institutionshave greater correlations with GOP which indicates that theyhave more impact on Chinarsquos marine economy

Therefore China needs to develop marine SampT espe-cially in research projects patents and research funds topromote marine economy and so as to make the economymore prosperous We need to further refine the NationalMarine EconomyDevelopment Plan to realize the sustainabledevelopment of marine economy in China and build Chinainto a maritime power

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The relevant researches done in this paper are supported bythe National Social Science FundMajor Projects (14ZDB151)General Financial Grant from theChina Postdoctoral ScienceFoundation (2015M580611) Qingdao Postdoctoral Appli-cation Research Project Funding (251) and FundamentalResearch Funds for the Central Universities (201613006201564031)

References

[1] J L Deng ldquoIntroduction to grey system theoryrdquoThe Journal ofGrey System vol 1 no 1 pp 1ndash24 1989

[2] L A Zadeh ldquoFuzzy algorithmsrdquo Information amp Control vol 12no 2 pp 94ndash102 1968

[3] Z Pawlak ldquoRough setsrdquo International Journal of Computer ampInformation Sciences vol 11 no 5 pp 341ndash356 1982

[4] P Liu L He and X Yu ldquoGeneralized hybrid aggregation opera-tors based on the 2-dimension uncertain linguistic informationfor multiple attribute group decision makingrdquo Group Decisionand Negotiation vol 25 no 1 pp 103ndash126 2016

[5] PD Liu Y Li and J Antucheviciene ldquoAmulti-criteria decision-making method based on intuitionistic trapezoidal fuzzy prior-itizedOWAoperatorrdquoTechnological and EconomicDevelopmentof Economy vol 22 no 3 pp 453ndash469 2016

[6] P Liu ldquoSome generalized dependent aggregation operators withintuitionistic linguistic numbers and their application to groupdecisionmakingrdquo Journal of Computer and System Sciences vol79 no 1 pp 131ndash143 2013

[7] P Liu and F Jin ldquoA multi-attribute group decision-makingmethod based on weighted geometric aggregation operators ofinterval-valued trapezoidal fuzzy numbersrdquoAppliedMathemat-ical Modelling vol 36 no 6 pp 2498ndash2509 2012

[8] P Liu X Zhang and F Jin ldquoA multi-attribute group decision-making method based on interval-valued trapezoidal fuzzynumbers hybrid harmonic averaging operatorsrdquo Journal ofIntelligent and Fuzzy Systems vol 23 no 5 pp 159ndash168 2012

[9] P Liu ldquoSome geometric aggregation operators based on intervalintuitionistic uncertain linguistic variables and their applicationto group decision makingrdquo Applied Mathematical Modellingvol 37 no 4 pp 2430ndash2444 2013

[10] J L Deng ldquoRelational space of grey theoryrdquo FuzzyMathematicsvol 4 no 2 pp 1ndash10 1985

[11] Z G Mei ldquoThe concept and computation method of greyabsolute correlation degreerdquo System Engineering no 05 pp 43ndash44 1992

[12] S F Liu Y G Dang Z G Fang et al Grey System Theory andApplication Science Press Beijing China 2012

[13] W X Tang ldquoThe concept and the computation method of Trsquoscorrelation degreerdquo Application of Statistics and Managementno 01 pp 34ndash37 1995

[14] Y G Dang ldquoResearch on grey relational analysis of sloperdquoSystem Sciences and Comprehensive Studies in Agriculture vol10 pp 331ndash337 1994

[15] Z L Wang and Q Y Wang ldquoSome properties of Grey B-relateddegreerdquo Journal of Hebei Mining and Civil Engineering Instituteno 3 pp 48ndash50 1992

[16] X H Zhao andQ YWang ldquoThe relational analysis of C-moderdquoJournal of Huazhong University of Science and Technology vol27 no 3 pp 75ndash77 1999

8 Mathematical Problems in Engineering

[17] H X Shi S F Liu Z G Fang et al ldquoThe model of greyperiodic incidence and their rehabilitationrdquo Chinese Journal ofManagement Science vol 3 pp 131ndash136 2008

[18] H Y Du H X Shi S F Liu et al ldquoStudy on the model ofgrey periodic incidence judged on sloperdquo Chinese Journal ofManagement Science no 01 pp 128ndash132 2010

[19] H J Xiong M Y Chen and T Qu ldquoSome extensions of greyrelational grade formulardquo Systems Engineering and Electronicsno 1 pp 8ndash10 2000

[20] Y G Dang S F Liu B Liu et al ldquoImprovement on degree ofgrey slope incidencerdquo Engineering Science vol 6 no 3 pp 41ndash44 2004

[21] Y G Sun and Y G Dang ldquoImproved model of slope greyrelational analysisrdquo Statistics and Decision no 15 pp 12ndash132007

[22] Y-G Sun and Y-G Dang ldquoImprovement on grey Trsquos correla-tion degreerdquo SystemEngineeringTheory and Practice vol 28 no4 pp 135ndash139 2008

[23] K Zhang and S-F Liu ldquoExtended clusters of grey incidencesfor panel data and its applicationrdquo System Engineering-Theory ampPractice vol 30 no 7 pp 1253ndash1259 2010

[24] X Li K W Hipel and Y Dang ldquoAn improved grey relationalanalysis approach for panel data clusteringrdquoExpert SystemswithApplications vol 42 no 23 pp 9105ndash9116 2015

[25] Y Wang X Shi J Sun and W Qian ldquoA grey interval relationaldegree-based dynamic multiattribute decision making methodand its application in investment decision makingrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 607016 6pages 2014

[26] Z Li G Wen and N Xie ldquoAn approach to fuzzy soft setsin decision making based on grey relational analysis andDempster-Shafer theory of evidence an application in medicaldiagnosisrdquo Artificial Intelligence in Medicine vol 64 no 3 pp161ndash171 2015

[27] S H Hashemi A Karimi and M Tavana ldquoAn integratedgreen supplier selection approachwith analytic network processand improved Grey relational analysisrdquo International Journal ofProduction Economics vol 159 pp 178ndash191 2015

[28] F L Wu F S Liu G L Yao et al ldquoFractional order greyrelational analysis and its applicationrdquo Scientia Iranica vol 22no 3 pp 1171ndash1178 2015

[29] X Guo Y Ni and Wangjia ldquoA grey relational analysis modelof scientific research ability on music based on AHP and itsrealizationrdquo International Journal of Signal Processing ImageProcessing amp Pattern Recognition vol 8 no 5 pp 211ndash222 2015

[30] G-W Wei ldquoGray relational analysis method for intuitionisticfuzzy multiple attribute decision makingrdquo Expert Systems withApplications vol 38 no 9 pp 11671ndash11677 2011

[31] X M Li Y G Dang and L Jin ldquoGrey trend analysis based ongrey relational degree with rate of change and its applicationrdquoChinese Journal of Management Science vol 23 no 9 pp 132ndash138 2015

[32] X Li Y Dang L Jin andWKang ldquoGCRAmodel for grey trendanalysis and its applicationrdquo Journal of Grey System vol 27 no1 pp 57ndash69 2015

[33] X M Li Y G Dang S Ding and J Zhang ldquoGrey accumula-tion generation relational analysis model for nonequidistanceunequal-length sequences and its applicationrdquo MathematicalProblems in Engineering vol 2014 Article ID 764857 8 pages2014

[34] G Q HuangW B Zhao and S H Xu ldquoA combinationmethodof improved grey relational degree and AHP for effectivenessevaluationrdquo in Proceedings of the 3rd International Conferenceon Mechatronics and Information Technology 2016

[35] X L Ning W U Ying-Xia Y U Tian-Peng et al ldquoResearchon comprehensive validation of simulation models based onimproved grey relational analysisrdquo Systems Engineering amp Elec-tronics vol 32 no 8 pp 1677ndash1679 2016

[36] N Xie Y Han and Z Li ldquoA novel approach to fuzzy soft sets indecision making based on grey relational analysis and MYCINcertainty factorrdquo International Journal of Computational Intelli-gence Systems vol 8 no 5 pp 959ndash976 2015

[37] W Wu and Y Peng ldquoExtension of grey relational analysis forfacilitating group consensus to oil spill emergency manage-mentrdquo Annals of Operations Research vol 238 no 1-2 pp 615ndash635 2016

[38] K Guo and Q Zhang ldquoDetecting communities in socialnetworks by local affinity propagation with grey relationalanalysisrdquo Grey Systems Theory and Application vol 5 no 1 pp31ndash40 2015

[39] X Liu and T Liu ldquoBlasting parameters optimization based ongrey relational analysisrdquo Gansu Metallurgy no 2 pp 1ndash3 2016

[40] NWang S X Zhang and J Cao ldquoApplication ofGrey relationalanalysis in evaluation of cross-fault deformation anomaly inter-ference factorsrdquo Journal of Seismological Research vol 38 no 1pp 90ndash98 2012

[41] J Qiao and J Zhu ldquoGovernment input to ocean science andtechnology and marine economic growth empirical studybased on panel datardquo Science and Technology ManagementResearch no 4 pp 37ndash40 2012

[42] B Dai G Jin and M Han ldquoAnalysis on temporal and spatialevolution of marine science and technology total factor pro-ductivity and its influencing factors in Chinese coastal areasrdquoGeographical Research vol 34 no 2 pp 328ndash340 2015

[43] R X Zhai and S O Business ldquoMarine science and technologyinvestment and marine economic growth an empirical studywith panel data in Chinarsquos coastal regionsrdquo Mathematics inPractice ampTheory no 4 pp 75ndash80 2014

[44] X X Zhang P F Zhang and X U Zi-Yi ldquoThe couplingevaluation model of Chinarsquos marine industrial aggregation andmarine science and technology talents aggregationrdquo Journal ofShandong University no 6 pp 118ndash128 2014

[45] D Liu X Li C Wang et al ldquoCalculating and forecasting ofmarine science and technology transfer raterdquoMarine Economyvol 5 no 2 pp 18ndash22 2015

[46] P Zhang X-R Li J-Y Zhang and Z-L Zhang ldquoIncludedangle distance of time series and similarity searchrdquo PatternRecognition and Artificial Intelligence vol 21 no 6 pp 763ndash7672008

[47] Y W Ding X H Yang A J Kavs et al ldquoSimilarity measure oftime series based on radian distancerdquo Journal of Electronics andInformation no 1 pp 122ndash128 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 3

relational analysis based on radian perspective (RPGRA) isproposed in this paper This new model can effectively usethe poor information in time series and can improve theaccuracy and validity of the research results RPGRA usespiecewise linear representation (PLR) to translate traditionalgrey relational degree into radian algorithm within differentpiecewise functions What is more RPGRA has the prop-erties of normativity uniqueness and parallelism and canexpand some existing models

RPGRA translates traditional grey relational degree intoradian algorithm by using PLR a method to analyze thenonlinear system by analyzing the nonlinear characteristicsas a piecewise linear approximation The nonlinear curve isreplaced by a straight line segment according to the differentsection Zhang et al proposed a measurement that the timeseries are represented approximately with a sequence of theincluded angles between a pair of neighboring line segments[46]Ding et al proposed a radian-distancewhich can reservesegment trend information when compared with the angle-distance [47] In a word RPGRA is put forward on thebase of the algorithm of radian-distance and traditional greyrelational degree and it is applied to analyze the relationshipbetween Chinarsquos marine SampT and economy

2 Establishment and Properties ofthe RPGRA Model

21 Establishment of the RPGRA Model The basic idea ofthe RPGRA model is to calculate the grey relational degreeaccording to the relative change trend of time series UsePLR to translate traditional grey relational degree into radianalgorithm within different piecewise functions Then applyradian-distance algorithm into grey relational analysis toestablish RPGRA model to calculate the grey relationaldegree

Step 1 (transforming the original time series) Time series isone kind of typical discrete sequences and it can be expressedin many ways using some methods In this paper time serieswill be expressed as the form of piecewise function based onthe thought of PLR

Therefore the time series can usually be expressed as thefollowing formula

119883119898= (119909119898(1199051) 119909119898(1199052)) (119909

119898(119905119894minus1) 119909119898(119905119894))

(119909119898(119905119899minus1) 119909119898(119905119899))

(1)

where 119905119894denotes the observation time points 119898 denotes the

number of time series 119899 denotes the number of observingtime points in one series119909

119898(119905119894)denotes the observation value

of the 119898th time series at 119905119894 and (119909

119898(119905119894minus1) 119909119898(119905119894)) denotes

the line segment with the starting value and the final value(Figure 1)

Definition 1 Segmented radian (rad) is the radian of theangle (acute angle) between the straight line formed by twoadjacent points in time series and timeline Set rad is positiveif the angle is in the first quadrant and it is negative if the angleis in the fourth quadrant

y

x1(t1)

x1(t2)

x1(t3)

x1(t4)

x1(t5)

1205721(t2)

1205721(t3)

1205721(t4)

t1 t2 t3 t4 t5 t

Figure 1 PLR of time series

Definition 2 Before setting the radian time series one shouldset angle series Set the time series that can be expressed as119883119898= 120572119898(1199052) 120572119898(1199053) 120572

119898(119905119899minus1) and one defines it as

the corresponding angle series of the time series where 119899denotes the number of observing time points in one seriesand 120572119898119905119894denotes the counterclockwise angle between the line

segments (119909119898(119905119894minus1) 119909119898(119905119894)) and (119909

119898(119905119894) 119909119898(119905119894+1)) of the 119898th

time seriesSet

rad119898(119905119896) = arctan

119909119898(119905119896+1) minus 119909119898(119905119896)

Δ119905 (2)

And it is the radian time series

Step 2 (calculating the radian variation) Assume the intervalis [119901 119902] and then set the following formula as the variationfunction of the corresponding radian series from 119905

119896minus1to

119905119896

119910119898(119905119896) = rad

119898(119905119896) minus rad

119898(119905119896minus1) 119896 = 1 2 119899 minus 2 (3)

Step 3 It is calculating the grey relational coefficient

Definition 3 Assume that 1198830= 1199090(1199051) 1199090(1199052) 119909

0(119905119899)

and 119883119894= 119909

119894(1199051) 119909119894(1199052) 119909

119894(119905119899) (119894 = 1 2 119898) are

sequences in [119901 119902] respectively the following formula willbe defined to calculate the relational coefficient between thesetwo time series

1205850119894(119896) =

1

1 +10038161003816100381610038161199100 (119905119896) minus 119910119894 (119905119896)

1003816100381610038161003816

(4)

In order to effectively distinguish the grey relational coef-ficient generated by two different time series a comparativevariable is introduced into formula (4) which is the subtrac-tion variable |119910

0(119905119896) minus 119910119894(119905119896)| When the variation function of

two time series in eachΔ119905119896is similar the comparative variable

will tend to be 0 and then 1205850119894(119896) will tend to be 1 and vice

versa

4 Mathematical Problems in Engineering

Table 1 Original data added value of strategic marine emerging industries Unit 100 million yuanitem

Year Gross oceanproduct

Marine scientificresearch

institutions

Research funds receiptsof the marine scientificresearch institutions

Marine scientificand technologicalresearch projects

Marine scientifictheses published

Marine scientificand technologicalpatents granted

2006 215924 136 52893 6593 8492 3792007 256187 136 77394 7617 9104 3982008 29718 135 87697 8327 9485 4412009 322776 186 16016 12600 14451 12502010 395727 181 195508 13466 14296 14822011 45496 179 232219 14253 15547 20342012 500452 177 257723 15403 16713 27462013 54313 175 265564 16331 16284 3430Source from 2006sim2014 China Marine Statistical Yearbook

Definition 4 Assuming that 1198830= 1199090(1199051) 1199090(1199052) 119909

0(119905119899)

and 119883119894= 119909119894(1199051) 119909119894(1199052) 119909

119894(119905119899) are nonnegative sequen-

ces in [119901 119902] then

1205850119894=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) (5)

is named the grey relational degree of the RPGRA of 1198830and

119883119894 The greater 120585

0119894is the stronger the correlation between119883

0

and119883119894is

22 Property of RPGRA

Theorem 5 The properties of the model of RPGRA are asfollows

(1) |1205850119894| le 1

(2) Symmetry 1205850119894= 1205851198940

(3) Uniqueness and independence 1205850119894being unique for two

fixed sequences and not influenced by other sequences(4) Comparability

Proof (1) We can obtain rad119898(119905119896) isin (minus1205872 1205872) from

Definition 1 so minus1 lt 119910119898(119905119896) lt 1 hArr minus1 le 120585

0119894(119905119896) le 1

119894 = 1 2 119898 119896 = 2 3 119899 and [119901 119902] = ⋃119899minus2119896=1Δ119905119896hArr minus1 le

1205850119894= (1(119902 minus 119901))sum

119899

119896=2Δ119905119896sdot 1205850119894(119905119896) le 1

(2) According to the definitions of the grey relationalcoefficient and the grey relational degree of the RPGRAproperty (2) is obvious

(3) The grey relational coefficient and the grey relationaldegree of the RPGRA are only connected with the twosequences involved Once the sequences are determined theradians are determined Therefore 120585

0119894of certain sequences

are confirmed and are not affected by other sequences in thesystem

(4) This property is also correct due to property (3)

Theorem 6 Assume that there are two time series 1198830=

1199090(1199051) 1199090(1199052) 119909

0(119905119899) and 119883

119894= 119909

119894(1199051) 119909119894(1199052)

119909119894(119905119899) (119894 = 1 2 119898) and their grey relational degree is 120585

0119894

which satisfies |1205850119894| le 1 and 120585

0119894= 1 if and only if 119883

119894(119905119896) =

1198830(119905119896) + 119888 (119896 = 1 2 119899 119888 is a constant) then119883

0and119883

119894are

parallel that is the RPGRA model satisfies the normativity ofGST

Proof As |1205850119894| le 1 and 120585

0119894= 1 hArr 120585

0119894(119905119896) = 1 hArr 119910

0(119905119896) =

119910119894(119905119896) hArr rad

0(119905119896) minus rad

0(119905119896minus1) = rad

119894(119905119896) minus rad

119894(119905119896minus1) hArr

rad0(119905119896) minus rad

0(1199051) = rad

119894(119905119896) minus rad

119894(1199051) hArr rad

119894(119905119896) =

rad0(119905119896) minus rad

0(1199051) + rad

119894(1199051) hArr rad

119894(119905119896) = rad

0(119905119896) + 119888 hArr

119883119894(119905119896) = 119883

0(119905119896) + 119888 hArr 119883

0119883119894are parallel And 119888 = rad

119894(1199051) minus

rad0(1199051)

That is themodel of RPGRA satisfies the characteristic ofGRArsquos normativity So this property was proved

3 Application of the RPGRAModel for Relationship between ChinarsquosSampT and Economy

In recent years Chinarsquos marine economy has been developingrapidly and marine science and technology have attractedhigh attention from concerned governmental departmentsAccording to the China Marine Statistical Yearbook theinvestment of marine science and technology has beenincreasing with the years In 2013 the research funds receiptsof the marine scientific research institutions are 265563million yuan increasing 200 from 2008 The research ofChinarsquos SampT is still in the initial stage There are few dataand they are mainly from China Marine Statistical YearbookTaking the choice of variables by scholars in Introductionand the availability of data into comprehensive considera-tion five variables are selected to represent Chinarsquos SampT toresearch their correlation with marine economyThey are thenumber of marine scientific research institutions researchfunds receipts of the marine scientific research institutionsthe number of marine scientific and technological researchprojects the number of marine scientific theses publishedand the number ofmarine scientific and technological patentsgranted

31 Empirical Analysis on Correlation between Chinarsquos MarineSampT and Economy The original data of Chinarsquos marinescience and technology and gross ocean product (GOP) areshown in Table 1

Use formula (2) to get the radian time series as Table 2

Mathematical Problems in Engineering 5

Table 2 The corresponding radian series of the original time series

Items rad119898(119905119896)

rad119898(1199052) rad

119898(1199053) rad

119898(1199054) rad

119898(1199055) rad

119898(1199056) rad

119898(1199057) rad

119898(1199058)

Gross ocean product 15705 15706 15704 15707 15706 15706 15706Research institutions 00000 minus07854 15512 minus13734 minus11071 minus11071 minus11071

Research funds receipts 15708 15708 minus15708 15708 15708 15708 15708

Research projects 15698 15694 15706 15696 15695 15699 15697

Theses published 15692 15682 15706 minus15643 15700 15699 minus15685

Patents granted 15182 15475 15696 15665 15690 15694 15693

Table 3 Correlation coefficient of Chinarsquos marine science and technology

Items 120585(119905119896)

120585(1199051) 120585(119905

2) 120585(119905

3) 120585(119905

4) 120585(119905

5) 120585(119905

6)

Research institutions 05601 02997 02548 07897 09999 10000Research funds receipts 10000 02415 02415 10000 09999 10000Research projects 09996 09987 09988 09999 09995 09998Theses published 09990 09974 02418 02419 10000 02416Patents granted 09715 09783 09967 09975 09995 10000

Use formulas (3) and (4) to calculate 120585(119905119896) as Table 3

Use GOP as a basic sequence to calculate the correlationcoefficient of the five variables for Chinarsquos marine science andtechnology

According to formula (5) 1205850119894is calculated as follows

12058501=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 06507

12058502=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 07471

12058503=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 09994

12058504=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 06203

12058505=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 09906

(6)

The RPGRA degree between GOP and marine scientificand technological research projects is 09994 ranked firstthe degree of marine scientific and technological patentsgranted is 09906 ranked second the degree of researchfunds receipts of the marine scientific research institutions is07471 ranked third the degree of marine scientific researchinstitutions is 06507 ranked fourth and the degree ofmarinescientific theses published is 06203 ranked the lastThe valueof grey relational degree does not have practical significanceso the results of empirical analysis are only concerned withthe ranking and do not rigidly adhere to the value

32 Conclusion of Empirical Analysis According to theempirical results GOP and marine scientific and technologi-cal research projects have a greater correlation degreemarine

0

5000

10000

15000

20000

Research institutions Research funds receiptsResearch projects Theses publishedPatents granted Gross ocean product

2007 2008 2009 2010 2011 2012 201320060

10000

20000

30000

40000

50000

60000

Figure 2 Diagrams of Chinarsquos marine science and technologySource from 2006sim2014 China Marine Statistical Yearbook NoteOnly the gross ocean product uses the secondary coordinate

scientific and technological patents granted take the secondplace followed by research funds receipts of the marinescientific research institutions and the degree of marinescientific theses published is the last one The geometricfigure of four variables and GOP is shown in Figure 2 Fromthe trend we can see that GOP and research funds receiptspatents granted and research projects have the most similartrend and have the least similarity with research institutionswhich conform to the results of the empirical analysis andillustrate the effectiveness of RPGRA model

33 Comparative Analysis with Traditional Grey RelationalMethods In this part some traditional GRAmodels are alsoused to make comparative analysis We use RPGRA degreeDengrsquos correlation degree absolute correlation degree rel-ative correlation degree and comprehensive correlationdegree The calculation result and ranking result are shownas Tables 4 and 5

6 Mathematical Problems in Engineering

Table 4 Grey relational degrees of different methods

DegreeMethods

RPGRA degree Dengrsquos correlationdegree

Absolutecorrelation degree

Relative correlationdegree

Comprehensivecorrelation degree

ItemsResearch institutions 06507 08706 05009 06752 05880Research funds receipts 07471 07410 05299 07161 06230Research projects 09994 09687 06688 09562 08125Theses published 06203 09325 06485 08887 07686Patents granted 09906 06734 05347 06355 05851

Table 5 Ranking results of the grey relational degree of different methods

Ranking resultsMethods

RPGRA degree Dengrsquos correlationdegree

Absolutecorrelation degree

Relative correlationdegree

Comprehensivecorrelation degree

ItemsResearch institutions 4 3 5 4 4Research funds receipts 3 4 4 3 3Research projects 1 1 1 1 1Theses published 5 2 2 2 2Patents granted 2 5 3 5 5

By analysis and calculation the ranking results are variantin different methods But in general the top one of therankings is research funds receipts and the number ofresearch institutions ranks in the last two which indicatesRPGRA modelrsquos validity and creditability The empiricalresults show that marine scientific and technological researchprojects marine scientific and technological patents grantedand research funds receipts of the marine scientific researchinstitutions have a greater correlation with GOP whichindicates that they have more impact on Chinarsquos marineeconomy

Marine scientific and technological research projectsinclude five parts basic research applied research experi-mental development result application and scientific andtechnological service The number of marine researchprojects has increased 96 from 2008 and its developmentsituation is shown as Table 6 Research projects can promotethe investigation of marine research and resources theconstruction of marine ecological civilization and mainte-nance of maritime rights and interests And they can alsoenhance the national marine awareness improve the capacityof marine infrastructure and equipment and then serveand promote the development of marine economy In thenext phase of the work State Oceanic Administration willaccelerate the research projects about construction of marinepower marine integrated management maintenance of themarine rights and interests and marine legislation

Marine scientific and technological patents of theresearch include the number of patent applications acceptedand the number of patents granted and in this paper we usethe number of patents granted because only it can reflectthe patent of marine science and technology in our country

accurately and objectively Intellectual property is theproduct of the commodity economy and the development ofscience and technology As one of the forms of intellectualproperty protection patent plays an important role in thedevelopment of science and technology The number ofmarine scientific and technological patents has increased30 compared with last year and the number is still growingrapidly

Research funds receipts of the marine scientific researchinstitutions include routine fund and loans in the governmentinvestment in the capital construction scientific and techno-logical activities The investment scale and structure of sci-entific research funds are shown as Figure 3 We can see thatroutine fund accounts for the largest proportion while loansand government investment occupy little floorTherefore theinvestment scale and structure are not reasonable and theyare an important factor affecting the conversion of scienceand technology achievements Furthermore due to its highcorrelation with marine economy it may affect the furtherdevelopment of marine economy

4 Conclusions and Policy Recommendations

The RPGRA model was established based on the similarityof the relative change trend of time series and on a newradian perspective Then it is applied to analysis of Chinarsquosmarine SampT and marine economyThe grey relational degreebetween marine SampT index and economy reflects its positionand function in marine economy Index with greater corre-lation degree will have a greater impact on the developmentof the marine economy Relevant data of marine SampT ischosen to analyze the relationship between Chinarsquos marine

Mathematical Problems in Engineering 7

Table 6 Development situation of marine scientific and technological research projects Unit item

Year Number ofresearch projects Basic research Applied research Experimental

development Result application Scientific andtechnological service

2008 8327 2087 2623 1420 691 15062009 12600 2753 3338 2550 1074 28852010 13466 3104 3497 2838 1359 26682011 14253 3476 3696 2855 1453 27732012 15403 3756 3854 3569 1515 27092013 16331 4276 3735 3997 1516 2807

2009 2010 2011 2012 2013

Routine fundLoans

Government investment

0

20

40

60

80

100

()

Figure 3 Diagrams of investment scale and structure of scientificresearch funds

SampT and marine economy The empirical results show thatmarine scientific and technological research projects marinescientific and technological patents granted and researchfunds receipts of the marine scientific research institutionshave greater correlations with GOP which indicates that theyhave more impact on Chinarsquos marine economy

Therefore China needs to develop marine SampT espe-cially in research projects patents and research funds topromote marine economy and so as to make the economymore prosperous We need to further refine the NationalMarine EconomyDevelopment Plan to realize the sustainabledevelopment of marine economy in China and build Chinainto a maritime power

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The relevant researches done in this paper are supported bythe National Social Science FundMajor Projects (14ZDB151)General Financial Grant from theChina Postdoctoral ScienceFoundation (2015M580611) Qingdao Postdoctoral Appli-cation Research Project Funding (251) and FundamentalResearch Funds for the Central Universities (201613006201564031)

References

[1] J L Deng ldquoIntroduction to grey system theoryrdquoThe Journal ofGrey System vol 1 no 1 pp 1ndash24 1989

[2] L A Zadeh ldquoFuzzy algorithmsrdquo Information amp Control vol 12no 2 pp 94ndash102 1968

[3] Z Pawlak ldquoRough setsrdquo International Journal of Computer ampInformation Sciences vol 11 no 5 pp 341ndash356 1982

[4] P Liu L He and X Yu ldquoGeneralized hybrid aggregation opera-tors based on the 2-dimension uncertain linguistic informationfor multiple attribute group decision makingrdquo Group Decisionand Negotiation vol 25 no 1 pp 103ndash126 2016

[5] PD Liu Y Li and J Antucheviciene ldquoAmulti-criteria decision-making method based on intuitionistic trapezoidal fuzzy prior-itizedOWAoperatorrdquoTechnological and EconomicDevelopmentof Economy vol 22 no 3 pp 453ndash469 2016

[6] P Liu ldquoSome generalized dependent aggregation operators withintuitionistic linguistic numbers and their application to groupdecisionmakingrdquo Journal of Computer and System Sciences vol79 no 1 pp 131ndash143 2013

[7] P Liu and F Jin ldquoA multi-attribute group decision-makingmethod based on weighted geometric aggregation operators ofinterval-valued trapezoidal fuzzy numbersrdquoAppliedMathemat-ical Modelling vol 36 no 6 pp 2498ndash2509 2012

[8] P Liu X Zhang and F Jin ldquoA multi-attribute group decision-making method based on interval-valued trapezoidal fuzzynumbers hybrid harmonic averaging operatorsrdquo Journal ofIntelligent and Fuzzy Systems vol 23 no 5 pp 159ndash168 2012

[9] P Liu ldquoSome geometric aggregation operators based on intervalintuitionistic uncertain linguistic variables and their applicationto group decision makingrdquo Applied Mathematical Modellingvol 37 no 4 pp 2430ndash2444 2013

[10] J L Deng ldquoRelational space of grey theoryrdquo FuzzyMathematicsvol 4 no 2 pp 1ndash10 1985

[11] Z G Mei ldquoThe concept and computation method of greyabsolute correlation degreerdquo System Engineering no 05 pp 43ndash44 1992

[12] S F Liu Y G Dang Z G Fang et al Grey System Theory andApplication Science Press Beijing China 2012

[13] W X Tang ldquoThe concept and the computation method of Trsquoscorrelation degreerdquo Application of Statistics and Managementno 01 pp 34ndash37 1995

[14] Y G Dang ldquoResearch on grey relational analysis of sloperdquoSystem Sciences and Comprehensive Studies in Agriculture vol10 pp 331ndash337 1994

[15] Z L Wang and Q Y Wang ldquoSome properties of Grey B-relateddegreerdquo Journal of Hebei Mining and Civil Engineering Instituteno 3 pp 48ndash50 1992

[16] X H Zhao andQ YWang ldquoThe relational analysis of C-moderdquoJournal of Huazhong University of Science and Technology vol27 no 3 pp 75ndash77 1999

8 Mathematical Problems in Engineering

[17] H X Shi S F Liu Z G Fang et al ldquoThe model of greyperiodic incidence and their rehabilitationrdquo Chinese Journal ofManagement Science vol 3 pp 131ndash136 2008

[18] H Y Du H X Shi S F Liu et al ldquoStudy on the model ofgrey periodic incidence judged on sloperdquo Chinese Journal ofManagement Science no 01 pp 128ndash132 2010

[19] H J Xiong M Y Chen and T Qu ldquoSome extensions of greyrelational grade formulardquo Systems Engineering and Electronicsno 1 pp 8ndash10 2000

[20] Y G Dang S F Liu B Liu et al ldquoImprovement on degree ofgrey slope incidencerdquo Engineering Science vol 6 no 3 pp 41ndash44 2004

[21] Y G Sun and Y G Dang ldquoImproved model of slope greyrelational analysisrdquo Statistics and Decision no 15 pp 12ndash132007

[22] Y-G Sun and Y-G Dang ldquoImprovement on grey Trsquos correla-tion degreerdquo SystemEngineeringTheory and Practice vol 28 no4 pp 135ndash139 2008

[23] K Zhang and S-F Liu ldquoExtended clusters of grey incidencesfor panel data and its applicationrdquo System Engineering-Theory ampPractice vol 30 no 7 pp 1253ndash1259 2010

[24] X Li K W Hipel and Y Dang ldquoAn improved grey relationalanalysis approach for panel data clusteringrdquoExpert SystemswithApplications vol 42 no 23 pp 9105ndash9116 2015

[25] Y Wang X Shi J Sun and W Qian ldquoA grey interval relationaldegree-based dynamic multiattribute decision making methodand its application in investment decision makingrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 607016 6pages 2014

[26] Z Li G Wen and N Xie ldquoAn approach to fuzzy soft setsin decision making based on grey relational analysis andDempster-Shafer theory of evidence an application in medicaldiagnosisrdquo Artificial Intelligence in Medicine vol 64 no 3 pp161ndash171 2015

[27] S H Hashemi A Karimi and M Tavana ldquoAn integratedgreen supplier selection approachwith analytic network processand improved Grey relational analysisrdquo International Journal ofProduction Economics vol 159 pp 178ndash191 2015

[28] F L Wu F S Liu G L Yao et al ldquoFractional order greyrelational analysis and its applicationrdquo Scientia Iranica vol 22no 3 pp 1171ndash1178 2015

[29] X Guo Y Ni and Wangjia ldquoA grey relational analysis modelof scientific research ability on music based on AHP and itsrealizationrdquo International Journal of Signal Processing ImageProcessing amp Pattern Recognition vol 8 no 5 pp 211ndash222 2015

[30] G-W Wei ldquoGray relational analysis method for intuitionisticfuzzy multiple attribute decision makingrdquo Expert Systems withApplications vol 38 no 9 pp 11671ndash11677 2011

[31] X M Li Y G Dang and L Jin ldquoGrey trend analysis based ongrey relational degree with rate of change and its applicationrdquoChinese Journal of Management Science vol 23 no 9 pp 132ndash138 2015

[32] X Li Y Dang L Jin andWKang ldquoGCRAmodel for grey trendanalysis and its applicationrdquo Journal of Grey System vol 27 no1 pp 57ndash69 2015

[33] X M Li Y G Dang S Ding and J Zhang ldquoGrey accumula-tion generation relational analysis model for nonequidistanceunequal-length sequences and its applicationrdquo MathematicalProblems in Engineering vol 2014 Article ID 764857 8 pages2014

[34] G Q HuangW B Zhao and S H Xu ldquoA combinationmethodof improved grey relational degree and AHP for effectivenessevaluationrdquo in Proceedings of the 3rd International Conferenceon Mechatronics and Information Technology 2016

[35] X L Ning W U Ying-Xia Y U Tian-Peng et al ldquoResearchon comprehensive validation of simulation models based onimproved grey relational analysisrdquo Systems Engineering amp Elec-tronics vol 32 no 8 pp 1677ndash1679 2016

[36] N Xie Y Han and Z Li ldquoA novel approach to fuzzy soft sets indecision making based on grey relational analysis and MYCINcertainty factorrdquo International Journal of Computational Intelli-gence Systems vol 8 no 5 pp 959ndash976 2015

[37] W Wu and Y Peng ldquoExtension of grey relational analysis forfacilitating group consensus to oil spill emergency manage-mentrdquo Annals of Operations Research vol 238 no 1-2 pp 615ndash635 2016

[38] K Guo and Q Zhang ldquoDetecting communities in socialnetworks by local affinity propagation with grey relationalanalysisrdquo Grey Systems Theory and Application vol 5 no 1 pp31ndash40 2015

[39] X Liu and T Liu ldquoBlasting parameters optimization based ongrey relational analysisrdquo Gansu Metallurgy no 2 pp 1ndash3 2016

[40] NWang S X Zhang and J Cao ldquoApplication ofGrey relationalanalysis in evaluation of cross-fault deformation anomaly inter-ference factorsrdquo Journal of Seismological Research vol 38 no 1pp 90ndash98 2012

[41] J Qiao and J Zhu ldquoGovernment input to ocean science andtechnology and marine economic growth empirical studybased on panel datardquo Science and Technology ManagementResearch no 4 pp 37ndash40 2012

[42] B Dai G Jin and M Han ldquoAnalysis on temporal and spatialevolution of marine science and technology total factor pro-ductivity and its influencing factors in Chinese coastal areasrdquoGeographical Research vol 34 no 2 pp 328ndash340 2015

[43] R X Zhai and S O Business ldquoMarine science and technologyinvestment and marine economic growth an empirical studywith panel data in Chinarsquos coastal regionsrdquo Mathematics inPractice ampTheory no 4 pp 75ndash80 2014

[44] X X Zhang P F Zhang and X U Zi-Yi ldquoThe couplingevaluation model of Chinarsquos marine industrial aggregation andmarine science and technology talents aggregationrdquo Journal ofShandong University no 6 pp 118ndash128 2014

[45] D Liu X Li C Wang et al ldquoCalculating and forecasting ofmarine science and technology transfer raterdquoMarine Economyvol 5 no 2 pp 18ndash22 2015

[46] P Zhang X-R Li J-Y Zhang and Z-L Zhang ldquoIncludedangle distance of time series and similarity searchrdquo PatternRecognition and Artificial Intelligence vol 21 no 6 pp 763ndash7672008

[47] Y W Ding X H Yang A J Kavs et al ldquoSimilarity measure oftime series based on radian distancerdquo Journal of Electronics andInformation no 1 pp 122ndash128 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

4 Mathematical Problems in Engineering

Table 1 Original data added value of strategic marine emerging industries Unit 100 million yuanitem

Year Gross oceanproduct

Marine scientificresearch

institutions

Research funds receiptsof the marine scientificresearch institutions

Marine scientificand technologicalresearch projects

Marine scientifictheses published

Marine scientificand technologicalpatents granted

2006 215924 136 52893 6593 8492 3792007 256187 136 77394 7617 9104 3982008 29718 135 87697 8327 9485 4412009 322776 186 16016 12600 14451 12502010 395727 181 195508 13466 14296 14822011 45496 179 232219 14253 15547 20342012 500452 177 257723 15403 16713 27462013 54313 175 265564 16331 16284 3430Source from 2006sim2014 China Marine Statistical Yearbook

Definition 4 Assuming that 1198830= 1199090(1199051) 1199090(1199052) 119909

0(119905119899)

and 119883119894= 119909119894(1199051) 119909119894(1199052) 119909

119894(119905119899) are nonnegative sequen-

ces in [119901 119902] then

1205850119894=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) (5)

is named the grey relational degree of the RPGRA of 1198830and

119883119894 The greater 120585

0119894is the stronger the correlation between119883

0

and119883119894is

22 Property of RPGRA

Theorem 5 The properties of the model of RPGRA are asfollows

(1) |1205850119894| le 1

(2) Symmetry 1205850119894= 1205851198940

(3) Uniqueness and independence 1205850119894being unique for two

fixed sequences and not influenced by other sequences(4) Comparability

Proof (1) We can obtain rad119898(119905119896) isin (minus1205872 1205872) from

Definition 1 so minus1 lt 119910119898(119905119896) lt 1 hArr minus1 le 120585

0119894(119905119896) le 1

119894 = 1 2 119898 119896 = 2 3 119899 and [119901 119902] = ⋃119899minus2119896=1Δ119905119896hArr minus1 le

1205850119894= (1(119902 minus 119901))sum

119899

119896=2Δ119905119896sdot 1205850119894(119905119896) le 1

(2) According to the definitions of the grey relationalcoefficient and the grey relational degree of the RPGRAproperty (2) is obvious

(3) The grey relational coefficient and the grey relationaldegree of the RPGRA are only connected with the twosequences involved Once the sequences are determined theradians are determined Therefore 120585

0119894of certain sequences

are confirmed and are not affected by other sequences in thesystem

(4) This property is also correct due to property (3)

Theorem 6 Assume that there are two time series 1198830=

1199090(1199051) 1199090(1199052) 119909

0(119905119899) and 119883

119894= 119909

119894(1199051) 119909119894(1199052)

119909119894(119905119899) (119894 = 1 2 119898) and their grey relational degree is 120585

0119894

which satisfies |1205850119894| le 1 and 120585

0119894= 1 if and only if 119883

119894(119905119896) =

1198830(119905119896) + 119888 (119896 = 1 2 119899 119888 is a constant) then119883

0and119883

119894are

parallel that is the RPGRA model satisfies the normativity ofGST

Proof As |1205850119894| le 1 and 120585

0119894= 1 hArr 120585

0119894(119905119896) = 1 hArr 119910

0(119905119896) =

119910119894(119905119896) hArr rad

0(119905119896) minus rad

0(119905119896minus1) = rad

119894(119905119896) minus rad

119894(119905119896minus1) hArr

rad0(119905119896) minus rad

0(1199051) = rad

119894(119905119896) minus rad

119894(1199051) hArr rad

119894(119905119896) =

rad0(119905119896) minus rad

0(1199051) + rad

119894(1199051) hArr rad

119894(119905119896) = rad

0(119905119896) + 119888 hArr

119883119894(119905119896) = 119883

0(119905119896) + 119888 hArr 119883

0119883119894are parallel And 119888 = rad

119894(1199051) minus

rad0(1199051)

That is themodel of RPGRA satisfies the characteristic ofGRArsquos normativity So this property was proved

3 Application of the RPGRAModel for Relationship between ChinarsquosSampT and Economy

In recent years Chinarsquos marine economy has been developingrapidly and marine science and technology have attractedhigh attention from concerned governmental departmentsAccording to the China Marine Statistical Yearbook theinvestment of marine science and technology has beenincreasing with the years In 2013 the research funds receiptsof the marine scientific research institutions are 265563million yuan increasing 200 from 2008 The research ofChinarsquos SampT is still in the initial stage There are few dataand they are mainly from China Marine Statistical YearbookTaking the choice of variables by scholars in Introductionand the availability of data into comprehensive considera-tion five variables are selected to represent Chinarsquos SampT toresearch their correlation with marine economyThey are thenumber of marine scientific research institutions researchfunds receipts of the marine scientific research institutionsthe number of marine scientific and technological researchprojects the number of marine scientific theses publishedand the number ofmarine scientific and technological patentsgranted

31 Empirical Analysis on Correlation between Chinarsquos MarineSampT and Economy The original data of Chinarsquos marinescience and technology and gross ocean product (GOP) areshown in Table 1

Use formula (2) to get the radian time series as Table 2

Mathematical Problems in Engineering 5

Table 2 The corresponding radian series of the original time series

Items rad119898(119905119896)

rad119898(1199052) rad

119898(1199053) rad

119898(1199054) rad

119898(1199055) rad

119898(1199056) rad

119898(1199057) rad

119898(1199058)

Gross ocean product 15705 15706 15704 15707 15706 15706 15706Research institutions 00000 minus07854 15512 minus13734 minus11071 minus11071 minus11071

Research funds receipts 15708 15708 minus15708 15708 15708 15708 15708

Research projects 15698 15694 15706 15696 15695 15699 15697

Theses published 15692 15682 15706 minus15643 15700 15699 minus15685

Patents granted 15182 15475 15696 15665 15690 15694 15693

Table 3 Correlation coefficient of Chinarsquos marine science and technology

Items 120585(119905119896)

120585(1199051) 120585(119905

2) 120585(119905

3) 120585(119905

4) 120585(119905

5) 120585(119905

6)

Research institutions 05601 02997 02548 07897 09999 10000Research funds receipts 10000 02415 02415 10000 09999 10000Research projects 09996 09987 09988 09999 09995 09998Theses published 09990 09974 02418 02419 10000 02416Patents granted 09715 09783 09967 09975 09995 10000

Use formulas (3) and (4) to calculate 120585(119905119896) as Table 3

Use GOP as a basic sequence to calculate the correlationcoefficient of the five variables for Chinarsquos marine science andtechnology

According to formula (5) 1205850119894is calculated as follows

12058501=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 06507

12058502=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 07471

12058503=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 09994

12058504=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 06203

12058505=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 09906

(6)

The RPGRA degree between GOP and marine scientificand technological research projects is 09994 ranked firstthe degree of marine scientific and technological patentsgranted is 09906 ranked second the degree of researchfunds receipts of the marine scientific research institutions is07471 ranked third the degree of marine scientific researchinstitutions is 06507 ranked fourth and the degree ofmarinescientific theses published is 06203 ranked the lastThe valueof grey relational degree does not have practical significanceso the results of empirical analysis are only concerned withthe ranking and do not rigidly adhere to the value

32 Conclusion of Empirical Analysis According to theempirical results GOP and marine scientific and technologi-cal research projects have a greater correlation degreemarine

0

5000

10000

15000

20000

Research institutions Research funds receiptsResearch projects Theses publishedPatents granted Gross ocean product

2007 2008 2009 2010 2011 2012 201320060

10000

20000

30000

40000

50000

60000

Figure 2 Diagrams of Chinarsquos marine science and technologySource from 2006sim2014 China Marine Statistical Yearbook NoteOnly the gross ocean product uses the secondary coordinate

scientific and technological patents granted take the secondplace followed by research funds receipts of the marinescientific research institutions and the degree of marinescientific theses published is the last one The geometricfigure of four variables and GOP is shown in Figure 2 Fromthe trend we can see that GOP and research funds receiptspatents granted and research projects have the most similartrend and have the least similarity with research institutionswhich conform to the results of the empirical analysis andillustrate the effectiveness of RPGRA model

33 Comparative Analysis with Traditional Grey RelationalMethods In this part some traditional GRAmodels are alsoused to make comparative analysis We use RPGRA degreeDengrsquos correlation degree absolute correlation degree rel-ative correlation degree and comprehensive correlationdegree The calculation result and ranking result are shownas Tables 4 and 5

6 Mathematical Problems in Engineering

Table 4 Grey relational degrees of different methods

DegreeMethods

RPGRA degree Dengrsquos correlationdegree

Absolutecorrelation degree

Relative correlationdegree

Comprehensivecorrelation degree

ItemsResearch institutions 06507 08706 05009 06752 05880Research funds receipts 07471 07410 05299 07161 06230Research projects 09994 09687 06688 09562 08125Theses published 06203 09325 06485 08887 07686Patents granted 09906 06734 05347 06355 05851

Table 5 Ranking results of the grey relational degree of different methods

Ranking resultsMethods

RPGRA degree Dengrsquos correlationdegree

Absolutecorrelation degree

Relative correlationdegree

Comprehensivecorrelation degree

ItemsResearch institutions 4 3 5 4 4Research funds receipts 3 4 4 3 3Research projects 1 1 1 1 1Theses published 5 2 2 2 2Patents granted 2 5 3 5 5

By analysis and calculation the ranking results are variantin different methods But in general the top one of therankings is research funds receipts and the number ofresearch institutions ranks in the last two which indicatesRPGRA modelrsquos validity and creditability The empiricalresults show that marine scientific and technological researchprojects marine scientific and technological patents grantedand research funds receipts of the marine scientific researchinstitutions have a greater correlation with GOP whichindicates that they have more impact on Chinarsquos marineeconomy

Marine scientific and technological research projectsinclude five parts basic research applied research experi-mental development result application and scientific andtechnological service The number of marine researchprojects has increased 96 from 2008 and its developmentsituation is shown as Table 6 Research projects can promotethe investigation of marine research and resources theconstruction of marine ecological civilization and mainte-nance of maritime rights and interests And they can alsoenhance the national marine awareness improve the capacityof marine infrastructure and equipment and then serveand promote the development of marine economy In thenext phase of the work State Oceanic Administration willaccelerate the research projects about construction of marinepower marine integrated management maintenance of themarine rights and interests and marine legislation

Marine scientific and technological patents of theresearch include the number of patent applications acceptedand the number of patents granted and in this paper we usethe number of patents granted because only it can reflectthe patent of marine science and technology in our country

accurately and objectively Intellectual property is theproduct of the commodity economy and the development ofscience and technology As one of the forms of intellectualproperty protection patent plays an important role in thedevelopment of science and technology The number ofmarine scientific and technological patents has increased30 compared with last year and the number is still growingrapidly

Research funds receipts of the marine scientific researchinstitutions include routine fund and loans in the governmentinvestment in the capital construction scientific and techno-logical activities The investment scale and structure of sci-entific research funds are shown as Figure 3 We can see thatroutine fund accounts for the largest proportion while loansand government investment occupy little floorTherefore theinvestment scale and structure are not reasonable and theyare an important factor affecting the conversion of scienceand technology achievements Furthermore due to its highcorrelation with marine economy it may affect the furtherdevelopment of marine economy

4 Conclusions and Policy Recommendations

The RPGRA model was established based on the similarityof the relative change trend of time series and on a newradian perspective Then it is applied to analysis of Chinarsquosmarine SampT and marine economyThe grey relational degreebetween marine SampT index and economy reflects its positionand function in marine economy Index with greater corre-lation degree will have a greater impact on the developmentof the marine economy Relevant data of marine SampT ischosen to analyze the relationship between Chinarsquos marine

Mathematical Problems in Engineering 7

Table 6 Development situation of marine scientific and technological research projects Unit item

Year Number ofresearch projects Basic research Applied research Experimental

development Result application Scientific andtechnological service

2008 8327 2087 2623 1420 691 15062009 12600 2753 3338 2550 1074 28852010 13466 3104 3497 2838 1359 26682011 14253 3476 3696 2855 1453 27732012 15403 3756 3854 3569 1515 27092013 16331 4276 3735 3997 1516 2807

2009 2010 2011 2012 2013

Routine fundLoans

Government investment

0

20

40

60

80

100

()

Figure 3 Diagrams of investment scale and structure of scientificresearch funds

SampT and marine economy The empirical results show thatmarine scientific and technological research projects marinescientific and technological patents granted and researchfunds receipts of the marine scientific research institutionshave greater correlations with GOP which indicates that theyhave more impact on Chinarsquos marine economy

Therefore China needs to develop marine SampT espe-cially in research projects patents and research funds topromote marine economy and so as to make the economymore prosperous We need to further refine the NationalMarine EconomyDevelopment Plan to realize the sustainabledevelopment of marine economy in China and build Chinainto a maritime power

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The relevant researches done in this paper are supported bythe National Social Science FundMajor Projects (14ZDB151)General Financial Grant from theChina Postdoctoral ScienceFoundation (2015M580611) Qingdao Postdoctoral Appli-cation Research Project Funding (251) and FundamentalResearch Funds for the Central Universities (201613006201564031)

References

[1] J L Deng ldquoIntroduction to grey system theoryrdquoThe Journal ofGrey System vol 1 no 1 pp 1ndash24 1989

[2] L A Zadeh ldquoFuzzy algorithmsrdquo Information amp Control vol 12no 2 pp 94ndash102 1968

[3] Z Pawlak ldquoRough setsrdquo International Journal of Computer ampInformation Sciences vol 11 no 5 pp 341ndash356 1982

[4] P Liu L He and X Yu ldquoGeneralized hybrid aggregation opera-tors based on the 2-dimension uncertain linguistic informationfor multiple attribute group decision makingrdquo Group Decisionand Negotiation vol 25 no 1 pp 103ndash126 2016

[5] PD Liu Y Li and J Antucheviciene ldquoAmulti-criteria decision-making method based on intuitionistic trapezoidal fuzzy prior-itizedOWAoperatorrdquoTechnological and EconomicDevelopmentof Economy vol 22 no 3 pp 453ndash469 2016

[6] P Liu ldquoSome generalized dependent aggregation operators withintuitionistic linguistic numbers and their application to groupdecisionmakingrdquo Journal of Computer and System Sciences vol79 no 1 pp 131ndash143 2013

[7] P Liu and F Jin ldquoA multi-attribute group decision-makingmethod based on weighted geometric aggregation operators ofinterval-valued trapezoidal fuzzy numbersrdquoAppliedMathemat-ical Modelling vol 36 no 6 pp 2498ndash2509 2012

[8] P Liu X Zhang and F Jin ldquoA multi-attribute group decision-making method based on interval-valued trapezoidal fuzzynumbers hybrid harmonic averaging operatorsrdquo Journal ofIntelligent and Fuzzy Systems vol 23 no 5 pp 159ndash168 2012

[9] P Liu ldquoSome geometric aggregation operators based on intervalintuitionistic uncertain linguistic variables and their applicationto group decision makingrdquo Applied Mathematical Modellingvol 37 no 4 pp 2430ndash2444 2013

[10] J L Deng ldquoRelational space of grey theoryrdquo FuzzyMathematicsvol 4 no 2 pp 1ndash10 1985

[11] Z G Mei ldquoThe concept and computation method of greyabsolute correlation degreerdquo System Engineering no 05 pp 43ndash44 1992

[12] S F Liu Y G Dang Z G Fang et al Grey System Theory andApplication Science Press Beijing China 2012

[13] W X Tang ldquoThe concept and the computation method of Trsquoscorrelation degreerdquo Application of Statistics and Managementno 01 pp 34ndash37 1995

[14] Y G Dang ldquoResearch on grey relational analysis of sloperdquoSystem Sciences and Comprehensive Studies in Agriculture vol10 pp 331ndash337 1994

[15] Z L Wang and Q Y Wang ldquoSome properties of Grey B-relateddegreerdquo Journal of Hebei Mining and Civil Engineering Instituteno 3 pp 48ndash50 1992

[16] X H Zhao andQ YWang ldquoThe relational analysis of C-moderdquoJournal of Huazhong University of Science and Technology vol27 no 3 pp 75ndash77 1999

8 Mathematical Problems in Engineering

[17] H X Shi S F Liu Z G Fang et al ldquoThe model of greyperiodic incidence and their rehabilitationrdquo Chinese Journal ofManagement Science vol 3 pp 131ndash136 2008

[18] H Y Du H X Shi S F Liu et al ldquoStudy on the model ofgrey periodic incidence judged on sloperdquo Chinese Journal ofManagement Science no 01 pp 128ndash132 2010

[19] H J Xiong M Y Chen and T Qu ldquoSome extensions of greyrelational grade formulardquo Systems Engineering and Electronicsno 1 pp 8ndash10 2000

[20] Y G Dang S F Liu B Liu et al ldquoImprovement on degree ofgrey slope incidencerdquo Engineering Science vol 6 no 3 pp 41ndash44 2004

[21] Y G Sun and Y G Dang ldquoImproved model of slope greyrelational analysisrdquo Statistics and Decision no 15 pp 12ndash132007

[22] Y-G Sun and Y-G Dang ldquoImprovement on grey Trsquos correla-tion degreerdquo SystemEngineeringTheory and Practice vol 28 no4 pp 135ndash139 2008

[23] K Zhang and S-F Liu ldquoExtended clusters of grey incidencesfor panel data and its applicationrdquo System Engineering-Theory ampPractice vol 30 no 7 pp 1253ndash1259 2010

[24] X Li K W Hipel and Y Dang ldquoAn improved grey relationalanalysis approach for panel data clusteringrdquoExpert SystemswithApplications vol 42 no 23 pp 9105ndash9116 2015

[25] Y Wang X Shi J Sun and W Qian ldquoA grey interval relationaldegree-based dynamic multiattribute decision making methodand its application in investment decision makingrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 607016 6pages 2014

[26] Z Li G Wen and N Xie ldquoAn approach to fuzzy soft setsin decision making based on grey relational analysis andDempster-Shafer theory of evidence an application in medicaldiagnosisrdquo Artificial Intelligence in Medicine vol 64 no 3 pp161ndash171 2015

[27] S H Hashemi A Karimi and M Tavana ldquoAn integratedgreen supplier selection approachwith analytic network processand improved Grey relational analysisrdquo International Journal ofProduction Economics vol 159 pp 178ndash191 2015

[28] F L Wu F S Liu G L Yao et al ldquoFractional order greyrelational analysis and its applicationrdquo Scientia Iranica vol 22no 3 pp 1171ndash1178 2015

[29] X Guo Y Ni and Wangjia ldquoA grey relational analysis modelof scientific research ability on music based on AHP and itsrealizationrdquo International Journal of Signal Processing ImageProcessing amp Pattern Recognition vol 8 no 5 pp 211ndash222 2015

[30] G-W Wei ldquoGray relational analysis method for intuitionisticfuzzy multiple attribute decision makingrdquo Expert Systems withApplications vol 38 no 9 pp 11671ndash11677 2011

[31] X M Li Y G Dang and L Jin ldquoGrey trend analysis based ongrey relational degree with rate of change and its applicationrdquoChinese Journal of Management Science vol 23 no 9 pp 132ndash138 2015

[32] X Li Y Dang L Jin andWKang ldquoGCRAmodel for grey trendanalysis and its applicationrdquo Journal of Grey System vol 27 no1 pp 57ndash69 2015

[33] X M Li Y G Dang S Ding and J Zhang ldquoGrey accumula-tion generation relational analysis model for nonequidistanceunequal-length sequences and its applicationrdquo MathematicalProblems in Engineering vol 2014 Article ID 764857 8 pages2014

[34] G Q HuangW B Zhao and S H Xu ldquoA combinationmethodof improved grey relational degree and AHP for effectivenessevaluationrdquo in Proceedings of the 3rd International Conferenceon Mechatronics and Information Technology 2016

[35] X L Ning W U Ying-Xia Y U Tian-Peng et al ldquoResearchon comprehensive validation of simulation models based onimproved grey relational analysisrdquo Systems Engineering amp Elec-tronics vol 32 no 8 pp 1677ndash1679 2016

[36] N Xie Y Han and Z Li ldquoA novel approach to fuzzy soft sets indecision making based on grey relational analysis and MYCINcertainty factorrdquo International Journal of Computational Intelli-gence Systems vol 8 no 5 pp 959ndash976 2015

[37] W Wu and Y Peng ldquoExtension of grey relational analysis forfacilitating group consensus to oil spill emergency manage-mentrdquo Annals of Operations Research vol 238 no 1-2 pp 615ndash635 2016

[38] K Guo and Q Zhang ldquoDetecting communities in socialnetworks by local affinity propagation with grey relationalanalysisrdquo Grey Systems Theory and Application vol 5 no 1 pp31ndash40 2015

[39] X Liu and T Liu ldquoBlasting parameters optimization based ongrey relational analysisrdquo Gansu Metallurgy no 2 pp 1ndash3 2016

[40] NWang S X Zhang and J Cao ldquoApplication ofGrey relationalanalysis in evaluation of cross-fault deformation anomaly inter-ference factorsrdquo Journal of Seismological Research vol 38 no 1pp 90ndash98 2012

[41] J Qiao and J Zhu ldquoGovernment input to ocean science andtechnology and marine economic growth empirical studybased on panel datardquo Science and Technology ManagementResearch no 4 pp 37ndash40 2012

[42] B Dai G Jin and M Han ldquoAnalysis on temporal and spatialevolution of marine science and technology total factor pro-ductivity and its influencing factors in Chinese coastal areasrdquoGeographical Research vol 34 no 2 pp 328ndash340 2015

[43] R X Zhai and S O Business ldquoMarine science and technologyinvestment and marine economic growth an empirical studywith panel data in Chinarsquos coastal regionsrdquo Mathematics inPractice ampTheory no 4 pp 75ndash80 2014

[44] X X Zhang P F Zhang and X U Zi-Yi ldquoThe couplingevaluation model of Chinarsquos marine industrial aggregation andmarine science and technology talents aggregationrdquo Journal ofShandong University no 6 pp 118ndash128 2014

[45] D Liu X Li C Wang et al ldquoCalculating and forecasting ofmarine science and technology transfer raterdquoMarine Economyvol 5 no 2 pp 18ndash22 2015

[46] P Zhang X-R Li J-Y Zhang and Z-L Zhang ldquoIncludedangle distance of time series and similarity searchrdquo PatternRecognition and Artificial Intelligence vol 21 no 6 pp 763ndash7672008

[47] Y W Ding X H Yang A J Kavs et al ldquoSimilarity measure oftime series based on radian distancerdquo Journal of Electronics andInformation no 1 pp 122ndash128 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 5

Table 2 The corresponding radian series of the original time series

Items rad119898(119905119896)

rad119898(1199052) rad

119898(1199053) rad

119898(1199054) rad

119898(1199055) rad

119898(1199056) rad

119898(1199057) rad

119898(1199058)

Gross ocean product 15705 15706 15704 15707 15706 15706 15706Research institutions 00000 minus07854 15512 minus13734 minus11071 minus11071 minus11071

Research funds receipts 15708 15708 minus15708 15708 15708 15708 15708

Research projects 15698 15694 15706 15696 15695 15699 15697

Theses published 15692 15682 15706 minus15643 15700 15699 minus15685

Patents granted 15182 15475 15696 15665 15690 15694 15693

Table 3 Correlation coefficient of Chinarsquos marine science and technology

Items 120585(119905119896)

120585(1199051) 120585(119905

2) 120585(119905

3) 120585(119905

4) 120585(119905

5) 120585(119905

6)

Research institutions 05601 02997 02548 07897 09999 10000Research funds receipts 10000 02415 02415 10000 09999 10000Research projects 09996 09987 09988 09999 09995 09998Theses published 09990 09974 02418 02419 10000 02416Patents granted 09715 09783 09967 09975 09995 10000

Use formulas (3) and (4) to calculate 120585(119905119896) as Table 3

Use GOP as a basic sequence to calculate the correlationcoefficient of the five variables for Chinarsquos marine science andtechnology

According to formula (5) 1205850119894is calculated as follows

12058501=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 06507

12058502=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 07471

12058503=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 09994

12058504=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 06203

12058505=1

119901 minus 119902

119899minus2

sum

119896=1

Δ119905119896sdot 120585 (119905119896) = 09906

(6)

The RPGRA degree between GOP and marine scientificand technological research projects is 09994 ranked firstthe degree of marine scientific and technological patentsgranted is 09906 ranked second the degree of researchfunds receipts of the marine scientific research institutions is07471 ranked third the degree of marine scientific researchinstitutions is 06507 ranked fourth and the degree ofmarinescientific theses published is 06203 ranked the lastThe valueof grey relational degree does not have practical significanceso the results of empirical analysis are only concerned withthe ranking and do not rigidly adhere to the value

32 Conclusion of Empirical Analysis According to theempirical results GOP and marine scientific and technologi-cal research projects have a greater correlation degreemarine

0

5000

10000

15000

20000

Research institutions Research funds receiptsResearch projects Theses publishedPatents granted Gross ocean product

2007 2008 2009 2010 2011 2012 201320060

10000

20000

30000

40000

50000

60000

Figure 2 Diagrams of Chinarsquos marine science and technologySource from 2006sim2014 China Marine Statistical Yearbook NoteOnly the gross ocean product uses the secondary coordinate

scientific and technological patents granted take the secondplace followed by research funds receipts of the marinescientific research institutions and the degree of marinescientific theses published is the last one The geometricfigure of four variables and GOP is shown in Figure 2 Fromthe trend we can see that GOP and research funds receiptspatents granted and research projects have the most similartrend and have the least similarity with research institutionswhich conform to the results of the empirical analysis andillustrate the effectiveness of RPGRA model

33 Comparative Analysis with Traditional Grey RelationalMethods In this part some traditional GRAmodels are alsoused to make comparative analysis We use RPGRA degreeDengrsquos correlation degree absolute correlation degree rel-ative correlation degree and comprehensive correlationdegree The calculation result and ranking result are shownas Tables 4 and 5

6 Mathematical Problems in Engineering

Table 4 Grey relational degrees of different methods

DegreeMethods

RPGRA degree Dengrsquos correlationdegree

Absolutecorrelation degree

Relative correlationdegree

Comprehensivecorrelation degree

ItemsResearch institutions 06507 08706 05009 06752 05880Research funds receipts 07471 07410 05299 07161 06230Research projects 09994 09687 06688 09562 08125Theses published 06203 09325 06485 08887 07686Patents granted 09906 06734 05347 06355 05851

Table 5 Ranking results of the grey relational degree of different methods

Ranking resultsMethods

RPGRA degree Dengrsquos correlationdegree

Absolutecorrelation degree

Relative correlationdegree

Comprehensivecorrelation degree

ItemsResearch institutions 4 3 5 4 4Research funds receipts 3 4 4 3 3Research projects 1 1 1 1 1Theses published 5 2 2 2 2Patents granted 2 5 3 5 5

By analysis and calculation the ranking results are variantin different methods But in general the top one of therankings is research funds receipts and the number ofresearch institutions ranks in the last two which indicatesRPGRA modelrsquos validity and creditability The empiricalresults show that marine scientific and technological researchprojects marine scientific and technological patents grantedand research funds receipts of the marine scientific researchinstitutions have a greater correlation with GOP whichindicates that they have more impact on Chinarsquos marineeconomy

Marine scientific and technological research projectsinclude five parts basic research applied research experi-mental development result application and scientific andtechnological service The number of marine researchprojects has increased 96 from 2008 and its developmentsituation is shown as Table 6 Research projects can promotethe investigation of marine research and resources theconstruction of marine ecological civilization and mainte-nance of maritime rights and interests And they can alsoenhance the national marine awareness improve the capacityof marine infrastructure and equipment and then serveand promote the development of marine economy In thenext phase of the work State Oceanic Administration willaccelerate the research projects about construction of marinepower marine integrated management maintenance of themarine rights and interests and marine legislation

Marine scientific and technological patents of theresearch include the number of patent applications acceptedand the number of patents granted and in this paper we usethe number of patents granted because only it can reflectthe patent of marine science and technology in our country

accurately and objectively Intellectual property is theproduct of the commodity economy and the development ofscience and technology As one of the forms of intellectualproperty protection patent plays an important role in thedevelopment of science and technology The number ofmarine scientific and technological patents has increased30 compared with last year and the number is still growingrapidly

Research funds receipts of the marine scientific researchinstitutions include routine fund and loans in the governmentinvestment in the capital construction scientific and techno-logical activities The investment scale and structure of sci-entific research funds are shown as Figure 3 We can see thatroutine fund accounts for the largest proportion while loansand government investment occupy little floorTherefore theinvestment scale and structure are not reasonable and theyare an important factor affecting the conversion of scienceand technology achievements Furthermore due to its highcorrelation with marine economy it may affect the furtherdevelopment of marine economy

4 Conclusions and Policy Recommendations

The RPGRA model was established based on the similarityof the relative change trend of time series and on a newradian perspective Then it is applied to analysis of Chinarsquosmarine SampT and marine economyThe grey relational degreebetween marine SampT index and economy reflects its positionand function in marine economy Index with greater corre-lation degree will have a greater impact on the developmentof the marine economy Relevant data of marine SampT ischosen to analyze the relationship between Chinarsquos marine

Mathematical Problems in Engineering 7

Table 6 Development situation of marine scientific and technological research projects Unit item

Year Number ofresearch projects Basic research Applied research Experimental

development Result application Scientific andtechnological service

2008 8327 2087 2623 1420 691 15062009 12600 2753 3338 2550 1074 28852010 13466 3104 3497 2838 1359 26682011 14253 3476 3696 2855 1453 27732012 15403 3756 3854 3569 1515 27092013 16331 4276 3735 3997 1516 2807

2009 2010 2011 2012 2013

Routine fundLoans

Government investment

0

20

40

60

80

100

()

Figure 3 Diagrams of investment scale and structure of scientificresearch funds

SampT and marine economy The empirical results show thatmarine scientific and technological research projects marinescientific and technological patents granted and researchfunds receipts of the marine scientific research institutionshave greater correlations with GOP which indicates that theyhave more impact on Chinarsquos marine economy

Therefore China needs to develop marine SampT espe-cially in research projects patents and research funds topromote marine economy and so as to make the economymore prosperous We need to further refine the NationalMarine EconomyDevelopment Plan to realize the sustainabledevelopment of marine economy in China and build Chinainto a maritime power

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The relevant researches done in this paper are supported bythe National Social Science FundMajor Projects (14ZDB151)General Financial Grant from theChina Postdoctoral ScienceFoundation (2015M580611) Qingdao Postdoctoral Appli-cation Research Project Funding (251) and FundamentalResearch Funds for the Central Universities (201613006201564031)

References

[1] J L Deng ldquoIntroduction to grey system theoryrdquoThe Journal ofGrey System vol 1 no 1 pp 1ndash24 1989

[2] L A Zadeh ldquoFuzzy algorithmsrdquo Information amp Control vol 12no 2 pp 94ndash102 1968

[3] Z Pawlak ldquoRough setsrdquo International Journal of Computer ampInformation Sciences vol 11 no 5 pp 341ndash356 1982

[4] P Liu L He and X Yu ldquoGeneralized hybrid aggregation opera-tors based on the 2-dimension uncertain linguistic informationfor multiple attribute group decision makingrdquo Group Decisionand Negotiation vol 25 no 1 pp 103ndash126 2016

[5] PD Liu Y Li and J Antucheviciene ldquoAmulti-criteria decision-making method based on intuitionistic trapezoidal fuzzy prior-itizedOWAoperatorrdquoTechnological and EconomicDevelopmentof Economy vol 22 no 3 pp 453ndash469 2016

[6] P Liu ldquoSome generalized dependent aggregation operators withintuitionistic linguistic numbers and their application to groupdecisionmakingrdquo Journal of Computer and System Sciences vol79 no 1 pp 131ndash143 2013

[7] P Liu and F Jin ldquoA multi-attribute group decision-makingmethod based on weighted geometric aggregation operators ofinterval-valued trapezoidal fuzzy numbersrdquoAppliedMathemat-ical Modelling vol 36 no 6 pp 2498ndash2509 2012

[8] P Liu X Zhang and F Jin ldquoA multi-attribute group decision-making method based on interval-valued trapezoidal fuzzynumbers hybrid harmonic averaging operatorsrdquo Journal ofIntelligent and Fuzzy Systems vol 23 no 5 pp 159ndash168 2012

[9] P Liu ldquoSome geometric aggregation operators based on intervalintuitionistic uncertain linguistic variables and their applicationto group decision makingrdquo Applied Mathematical Modellingvol 37 no 4 pp 2430ndash2444 2013

[10] J L Deng ldquoRelational space of grey theoryrdquo FuzzyMathematicsvol 4 no 2 pp 1ndash10 1985

[11] Z G Mei ldquoThe concept and computation method of greyabsolute correlation degreerdquo System Engineering no 05 pp 43ndash44 1992

[12] S F Liu Y G Dang Z G Fang et al Grey System Theory andApplication Science Press Beijing China 2012

[13] W X Tang ldquoThe concept and the computation method of Trsquoscorrelation degreerdquo Application of Statistics and Managementno 01 pp 34ndash37 1995

[14] Y G Dang ldquoResearch on grey relational analysis of sloperdquoSystem Sciences and Comprehensive Studies in Agriculture vol10 pp 331ndash337 1994

[15] Z L Wang and Q Y Wang ldquoSome properties of Grey B-relateddegreerdquo Journal of Hebei Mining and Civil Engineering Instituteno 3 pp 48ndash50 1992

[16] X H Zhao andQ YWang ldquoThe relational analysis of C-moderdquoJournal of Huazhong University of Science and Technology vol27 no 3 pp 75ndash77 1999

8 Mathematical Problems in Engineering

[17] H X Shi S F Liu Z G Fang et al ldquoThe model of greyperiodic incidence and their rehabilitationrdquo Chinese Journal ofManagement Science vol 3 pp 131ndash136 2008

[18] H Y Du H X Shi S F Liu et al ldquoStudy on the model ofgrey periodic incidence judged on sloperdquo Chinese Journal ofManagement Science no 01 pp 128ndash132 2010

[19] H J Xiong M Y Chen and T Qu ldquoSome extensions of greyrelational grade formulardquo Systems Engineering and Electronicsno 1 pp 8ndash10 2000

[20] Y G Dang S F Liu B Liu et al ldquoImprovement on degree ofgrey slope incidencerdquo Engineering Science vol 6 no 3 pp 41ndash44 2004

[21] Y G Sun and Y G Dang ldquoImproved model of slope greyrelational analysisrdquo Statistics and Decision no 15 pp 12ndash132007

[22] Y-G Sun and Y-G Dang ldquoImprovement on grey Trsquos correla-tion degreerdquo SystemEngineeringTheory and Practice vol 28 no4 pp 135ndash139 2008

[23] K Zhang and S-F Liu ldquoExtended clusters of grey incidencesfor panel data and its applicationrdquo System Engineering-Theory ampPractice vol 30 no 7 pp 1253ndash1259 2010

[24] X Li K W Hipel and Y Dang ldquoAn improved grey relationalanalysis approach for panel data clusteringrdquoExpert SystemswithApplications vol 42 no 23 pp 9105ndash9116 2015

[25] Y Wang X Shi J Sun and W Qian ldquoA grey interval relationaldegree-based dynamic multiattribute decision making methodand its application in investment decision makingrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 607016 6pages 2014

[26] Z Li G Wen and N Xie ldquoAn approach to fuzzy soft setsin decision making based on grey relational analysis andDempster-Shafer theory of evidence an application in medicaldiagnosisrdquo Artificial Intelligence in Medicine vol 64 no 3 pp161ndash171 2015

[27] S H Hashemi A Karimi and M Tavana ldquoAn integratedgreen supplier selection approachwith analytic network processand improved Grey relational analysisrdquo International Journal ofProduction Economics vol 159 pp 178ndash191 2015

[28] F L Wu F S Liu G L Yao et al ldquoFractional order greyrelational analysis and its applicationrdquo Scientia Iranica vol 22no 3 pp 1171ndash1178 2015

[29] X Guo Y Ni and Wangjia ldquoA grey relational analysis modelof scientific research ability on music based on AHP and itsrealizationrdquo International Journal of Signal Processing ImageProcessing amp Pattern Recognition vol 8 no 5 pp 211ndash222 2015

[30] G-W Wei ldquoGray relational analysis method for intuitionisticfuzzy multiple attribute decision makingrdquo Expert Systems withApplications vol 38 no 9 pp 11671ndash11677 2011

[31] X M Li Y G Dang and L Jin ldquoGrey trend analysis based ongrey relational degree with rate of change and its applicationrdquoChinese Journal of Management Science vol 23 no 9 pp 132ndash138 2015

[32] X Li Y Dang L Jin andWKang ldquoGCRAmodel for grey trendanalysis and its applicationrdquo Journal of Grey System vol 27 no1 pp 57ndash69 2015

[33] X M Li Y G Dang S Ding and J Zhang ldquoGrey accumula-tion generation relational analysis model for nonequidistanceunequal-length sequences and its applicationrdquo MathematicalProblems in Engineering vol 2014 Article ID 764857 8 pages2014

[34] G Q HuangW B Zhao and S H Xu ldquoA combinationmethodof improved grey relational degree and AHP for effectivenessevaluationrdquo in Proceedings of the 3rd International Conferenceon Mechatronics and Information Technology 2016

[35] X L Ning W U Ying-Xia Y U Tian-Peng et al ldquoResearchon comprehensive validation of simulation models based onimproved grey relational analysisrdquo Systems Engineering amp Elec-tronics vol 32 no 8 pp 1677ndash1679 2016

[36] N Xie Y Han and Z Li ldquoA novel approach to fuzzy soft sets indecision making based on grey relational analysis and MYCINcertainty factorrdquo International Journal of Computational Intelli-gence Systems vol 8 no 5 pp 959ndash976 2015

[37] W Wu and Y Peng ldquoExtension of grey relational analysis forfacilitating group consensus to oil spill emergency manage-mentrdquo Annals of Operations Research vol 238 no 1-2 pp 615ndash635 2016

[38] K Guo and Q Zhang ldquoDetecting communities in socialnetworks by local affinity propagation with grey relationalanalysisrdquo Grey Systems Theory and Application vol 5 no 1 pp31ndash40 2015

[39] X Liu and T Liu ldquoBlasting parameters optimization based ongrey relational analysisrdquo Gansu Metallurgy no 2 pp 1ndash3 2016

[40] NWang S X Zhang and J Cao ldquoApplication ofGrey relationalanalysis in evaluation of cross-fault deformation anomaly inter-ference factorsrdquo Journal of Seismological Research vol 38 no 1pp 90ndash98 2012

[41] J Qiao and J Zhu ldquoGovernment input to ocean science andtechnology and marine economic growth empirical studybased on panel datardquo Science and Technology ManagementResearch no 4 pp 37ndash40 2012

[42] B Dai G Jin and M Han ldquoAnalysis on temporal and spatialevolution of marine science and technology total factor pro-ductivity and its influencing factors in Chinese coastal areasrdquoGeographical Research vol 34 no 2 pp 328ndash340 2015

[43] R X Zhai and S O Business ldquoMarine science and technologyinvestment and marine economic growth an empirical studywith panel data in Chinarsquos coastal regionsrdquo Mathematics inPractice ampTheory no 4 pp 75ndash80 2014

[44] X X Zhang P F Zhang and X U Zi-Yi ldquoThe couplingevaluation model of Chinarsquos marine industrial aggregation andmarine science and technology talents aggregationrdquo Journal ofShandong University no 6 pp 118ndash128 2014

[45] D Liu X Li C Wang et al ldquoCalculating and forecasting ofmarine science and technology transfer raterdquoMarine Economyvol 5 no 2 pp 18ndash22 2015

[46] P Zhang X-R Li J-Y Zhang and Z-L Zhang ldquoIncludedangle distance of time series and similarity searchrdquo PatternRecognition and Artificial Intelligence vol 21 no 6 pp 763ndash7672008

[47] Y W Ding X H Yang A J Kavs et al ldquoSimilarity measure oftime series based on radian distancerdquo Journal of Electronics andInformation no 1 pp 122ndash128 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

6 Mathematical Problems in Engineering

Table 4 Grey relational degrees of different methods

DegreeMethods

RPGRA degree Dengrsquos correlationdegree

Absolutecorrelation degree

Relative correlationdegree

Comprehensivecorrelation degree

ItemsResearch institutions 06507 08706 05009 06752 05880Research funds receipts 07471 07410 05299 07161 06230Research projects 09994 09687 06688 09562 08125Theses published 06203 09325 06485 08887 07686Patents granted 09906 06734 05347 06355 05851

Table 5 Ranking results of the grey relational degree of different methods

Ranking resultsMethods

RPGRA degree Dengrsquos correlationdegree

Absolutecorrelation degree

Relative correlationdegree

Comprehensivecorrelation degree

ItemsResearch institutions 4 3 5 4 4Research funds receipts 3 4 4 3 3Research projects 1 1 1 1 1Theses published 5 2 2 2 2Patents granted 2 5 3 5 5

By analysis and calculation the ranking results are variantin different methods But in general the top one of therankings is research funds receipts and the number ofresearch institutions ranks in the last two which indicatesRPGRA modelrsquos validity and creditability The empiricalresults show that marine scientific and technological researchprojects marine scientific and technological patents grantedand research funds receipts of the marine scientific researchinstitutions have a greater correlation with GOP whichindicates that they have more impact on Chinarsquos marineeconomy

Marine scientific and technological research projectsinclude five parts basic research applied research experi-mental development result application and scientific andtechnological service The number of marine researchprojects has increased 96 from 2008 and its developmentsituation is shown as Table 6 Research projects can promotethe investigation of marine research and resources theconstruction of marine ecological civilization and mainte-nance of maritime rights and interests And they can alsoenhance the national marine awareness improve the capacityof marine infrastructure and equipment and then serveand promote the development of marine economy In thenext phase of the work State Oceanic Administration willaccelerate the research projects about construction of marinepower marine integrated management maintenance of themarine rights and interests and marine legislation

Marine scientific and technological patents of theresearch include the number of patent applications acceptedand the number of patents granted and in this paper we usethe number of patents granted because only it can reflectthe patent of marine science and technology in our country

accurately and objectively Intellectual property is theproduct of the commodity economy and the development ofscience and technology As one of the forms of intellectualproperty protection patent plays an important role in thedevelopment of science and technology The number ofmarine scientific and technological patents has increased30 compared with last year and the number is still growingrapidly

Research funds receipts of the marine scientific researchinstitutions include routine fund and loans in the governmentinvestment in the capital construction scientific and techno-logical activities The investment scale and structure of sci-entific research funds are shown as Figure 3 We can see thatroutine fund accounts for the largest proportion while loansand government investment occupy little floorTherefore theinvestment scale and structure are not reasonable and theyare an important factor affecting the conversion of scienceand technology achievements Furthermore due to its highcorrelation with marine economy it may affect the furtherdevelopment of marine economy

4 Conclusions and Policy Recommendations

The RPGRA model was established based on the similarityof the relative change trend of time series and on a newradian perspective Then it is applied to analysis of Chinarsquosmarine SampT and marine economyThe grey relational degreebetween marine SampT index and economy reflects its positionand function in marine economy Index with greater corre-lation degree will have a greater impact on the developmentof the marine economy Relevant data of marine SampT ischosen to analyze the relationship between Chinarsquos marine

Mathematical Problems in Engineering 7

Table 6 Development situation of marine scientific and technological research projects Unit item

Year Number ofresearch projects Basic research Applied research Experimental

development Result application Scientific andtechnological service

2008 8327 2087 2623 1420 691 15062009 12600 2753 3338 2550 1074 28852010 13466 3104 3497 2838 1359 26682011 14253 3476 3696 2855 1453 27732012 15403 3756 3854 3569 1515 27092013 16331 4276 3735 3997 1516 2807

2009 2010 2011 2012 2013

Routine fundLoans

Government investment

0

20

40

60

80

100

()

Figure 3 Diagrams of investment scale and structure of scientificresearch funds

SampT and marine economy The empirical results show thatmarine scientific and technological research projects marinescientific and technological patents granted and researchfunds receipts of the marine scientific research institutionshave greater correlations with GOP which indicates that theyhave more impact on Chinarsquos marine economy

Therefore China needs to develop marine SampT espe-cially in research projects patents and research funds topromote marine economy and so as to make the economymore prosperous We need to further refine the NationalMarine EconomyDevelopment Plan to realize the sustainabledevelopment of marine economy in China and build Chinainto a maritime power

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The relevant researches done in this paper are supported bythe National Social Science FundMajor Projects (14ZDB151)General Financial Grant from theChina Postdoctoral ScienceFoundation (2015M580611) Qingdao Postdoctoral Appli-cation Research Project Funding (251) and FundamentalResearch Funds for the Central Universities (201613006201564031)

References

[1] J L Deng ldquoIntroduction to grey system theoryrdquoThe Journal ofGrey System vol 1 no 1 pp 1ndash24 1989

[2] L A Zadeh ldquoFuzzy algorithmsrdquo Information amp Control vol 12no 2 pp 94ndash102 1968

[3] Z Pawlak ldquoRough setsrdquo International Journal of Computer ampInformation Sciences vol 11 no 5 pp 341ndash356 1982

[4] P Liu L He and X Yu ldquoGeneralized hybrid aggregation opera-tors based on the 2-dimension uncertain linguistic informationfor multiple attribute group decision makingrdquo Group Decisionand Negotiation vol 25 no 1 pp 103ndash126 2016

[5] PD Liu Y Li and J Antucheviciene ldquoAmulti-criteria decision-making method based on intuitionistic trapezoidal fuzzy prior-itizedOWAoperatorrdquoTechnological and EconomicDevelopmentof Economy vol 22 no 3 pp 453ndash469 2016

[6] P Liu ldquoSome generalized dependent aggregation operators withintuitionistic linguistic numbers and their application to groupdecisionmakingrdquo Journal of Computer and System Sciences vol79 no 1 pp 131ndash143 2013

[7] P Liu and F Jin ldquoA multi-attribute group decision-makingmethod based on weighted geometric aggregation operators ofinterval-valued trapezoidal fuzzy numbersrdquoAppliedMathemat-ical Modelling vol 36 no 6 pp 2498ndash2509 2012

[8] P Liu X Zhang and F Jin ldquoA multi-attribute group decision-making method based on interval-valued trapezoidal fuzzynumbers hybrid harmonic averaging operatorsrdquo Journal ofIntelligent and Fuzzy Systems vol 23 no 5 pp 159ndash168 2012

[9] P Liu ldquoSome geometric aggregation operators based on intervalintuitionistic uncertain linguistic variables and their applicationto group decision makingrdquo Applied Mathematical Modellingvol 37 no 4 pp 2430ndash2444 2013

[10] J L Deng ldquoRelational space of grey theoryrdquo FuzzyMathematicsvol 4 no 2 pp 1ndash10 1985

[11] Z G Mei ldquoThe concept and computation method of greyabsolute correlation degreerdquo System Engineering no 05 pp 43ndash44 1992

[12] S F Liu Y G Dang Z G Fang et al Grey System Theory andApplication Science Press Beijing China 2012

[13] W X Tang ldquoThe concept and the computation method of Trsquoscorrelation degreerdquo Application of Statistics and Managementno 01 pp 34ndash37 1995

[14] Y G Dang ldquoResearch on grey relational analysis of sloperdquoSystem Sciences and Comprehensive Studies in Agriculture vol10 pp 331ndash337 1994

[15] Z L Wang and Q Y Wang ldquoSome properties of Grey B-relateddegreerdquo Journal of Hebei Mining and Civil Engineering Instituteno 3 pp 48ndash50 1992

[16] X H Zhao andQ YWang ldquoThe relational analysis of C-moderdquoJournal of Huazhong University of Science and Technology vol27 no 3 pp 75ndash77 1999

8 Mathematical Problems in Engineering

[17] H X Shi S F Liu Z G Fang et al ldquoThe model of greyperiodic incidence and their rehabilitationrdquo Chinese Journal ofManagement Science vol 3 pp 131ndash136 2008

[18] H Y Du H X Shi S F Liu et al ldquoStudy on the model ofgrey periodic incidence judged on sloperdquo Chinese Journal ofManagement Science no 01 pp 128ndash132 2010

[19] H J Xiong M Y Chen and T Qu ldquoSome extensions of greyrelational grade formulardquo Systems Engineering and Electronicsno 1 pp 8ndash10 2000

[20] Y G Dang S F Liu B Liu et al ldquoImprovement on degree ofgrey slope incidencerdquo Engineering Science vol 6 no 3 pp 41ndash44 2004

[21] Y G Sun and Y G Dang ldquoImproved model of slope greyrelational analysisrdquo Statistics and Decision no 15 pp 12ndash132007

[22] Y-G Sun and Y-G Dang ldquoImprovement on grey Trsquos correla-tion degreerdquo SystemEngineeringTheory and Practice vol 28 no4 pp 135ndash139 2008

[23] K Zhang and S-F Liu ldquoExtended clusters of grey incidencesfor panel data and its applicationrdquo System Engineering-Theory ampPractice vol 30 no 7 pp 1253ndash1259 2010

[24] X Li K W Hipel and Y Dang ldquoAn improved grey relationalanalysis approach for panel data clusteringrdquoExpert SystemswithApplications vol 42 no 23 pp 9105ndash9116 2015

[25] Y Wang X Shi J Sun and W Qian ldquoA grey interval relationaldegree-based dynamic multiattribute decision making methodand its application in investment decision makingrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 607016 6pages 2014

[26] Z Li G Wen and N Xie ldquoAn approach to fuzzy soft setsin decision making based on grey relational analysis andDempster-Shafer theory of evidence an application in medicaldiagnosisrdquo Artificial Intelligence in Medicine vol 64 no 3 pp161ndash171 2015

[27] S H Hashemi A Karimi and M Tavana ldquoAn integratedgreen supplier selection approachwith analytic network processand improved Grey relational analysisrdquo International Journal ofProduction Economics vol 159 pp 178ndash191 2015

[28] F L Wu F S Liu G L Yao et al ldquoFractional order greyrelational analysis and its applicationrdquo Scientia Iranica vol 22no 3 pp 1171ndash1178 2015

[29] X Guo Y Ni and Wangjia ldquoA grey relational analysis modelof scientific research ability on music based on AHP and itsrealizationrdquo International Journal of Signal Processing ImageProcessing amp Pattern Recognition vol 8 no 5 pp 211ndash222 2015

[30] G-W Wei ldquoGray relational analysis method for intuitionisticfuzzy multiple attribute decision makingrdquo Expert Systems withApplications vol 38 no 9 pp 11671ndash11677 2011

[31] X M Li Y G Dang and L Jin ldquoGrey trend analysis based ongrey relational degree with rate of change and its applicationrdquoChinese Journal of Management Science vol 23 no 9 pp 132ndash138 2015

[32] X Li Y Dang L Jin andWKang ldquoGCRAmodel for grey trendanalysis and its applicationrdquo Journal of Grey System vol 27 no1 pp 57ndash69 2015

[33] X M Li Y G Dang S Ding and J Zhang ldquoGrey accumula-tion generation relational analysis model for nonequidistanceunequal-length sequences and its applicationrdquo MathematicalProblems in Engineering vol 2014 Article ID 764857 8 pages2014

[34] G Q HuangW B Zhao and S H Xu ldquoA combinationmethodof improved grey relational degree and AHP for effectivenessevaluationrdquo in Proceedings of the 3rd International Conferenceon Mechatronics and Information Technology 2016

[35] X L Ning W U Ying-Xia Y U Tian-Peng et al ldquoResearchon comprehensive validation of simulation models based onimproved grey relational analysisrdquo Systems Engineering amp Elec-tronics vol 32 no 8 pp 1677ndash1679 2016

[36] N Xie Y Han and Z Li ldquoA novel approach to fuzzy soft sets indecision making based on grey relational analysis and MYCINcertainty factorrdquo International Journal of Computational Intelli-gence Systems vol 8 no 5 pp 959ndash976 2015

[37] W Wu and Y Peng ldquoExtension of grey relational analysis forfacilitating group consensus to oil spill emergency manage-mentrdquo Annals of Operations Research vol 238 no 1-2 pp 615ndash635 2016

[38] K Guo and Q Zhang ldquoDetecting communities in socialnetworks by local affinity propagation with grey relationalanalysisrdquo Grey Systems Theory and Application vol 5 no 1 pp31ndash40 2015

[39] X Liu and T Liu ldquoBlasting parameters optimization based ongrey relational analysisrdquo Gansu Metallurgy no 2 pp 1ndash3 2016

[40] NWang S X Zhang and J Cao ldquoApplication ofGrey relationalanalysis in evaluation of cross-fault deformation anomaly inter-ference factorsrdquo Journal of Seismological Research vol 38 no 1pp 90ndash98 2012

[41] J Qiao and J Zhu ldquoGovernment input to ocean science andtechnology and marine economic growth empirical studybased on panel datardquo Science and Technology ManagementResearch no 4 pp 37ndash40 2012

[42] B Dai G Jin and M Han ldquoAnalysis on temporal and spatialevolution of marine science and technology total factor pro-ductivity and its influencing factors in Chinese coastal areasrdquoGeographical Research vol 34 no 2 pp 328ndash340 2015

[43] R X Zhai and S O Business ldquoMarine science and technologyinvestment and marine economic growth an empirical studywith panel data in Chinarsquos coastal regionsrdquo Mathematics inPractice ampTheory no 4 pp 75ndash80 2014

[44] X X Zhang P F Zhang and X U Zi-Yi ldquoThe couplingevaluation model of Chinarsquos marine industrial aggregation andmarine science and technology talents aggregationrdquo Journal ofShandong University no 6 pp 118ndash128 2014

[45] D Liu X Li C Wang et al ldquoCalculating and forecasting ofmarine science and technology transfer raterdquoMarine Economyvol 5 no 2 pp 18ndash22 2015

[46] P Zhang X-R Li J-Y Zhang and Z-L Zhang ldquoIncludedangle distance of time series and similarity searchrdquo PatternRecognition and Artificial Intelligence vol 21 no 6 pp 763ndash7672008

[47] Y W Ding X H Yang A J Kavs et al ldquoSimilarity measure oftime series based on radian distancerdquo Journal of Electronics andInformation no 1 pp 122ndash128 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 7

Table 6 Development situation of marine scientific and technological research projects Unit item

Year Number ofresearch projects Basic research Applied research Experimental

development Result application Scientific andtechnological service

2008 8327 2087 2623 1420 691 15062009 12600 2753 3338 2550 1074 28852010 13466 3104 3497 2838 1359 26682011 14253 3476 3696 2855 1453 27732012 15403 3756 3854 3569 1515 27092013 16331 4276 3735 3997 1516 2807

2009 2010 2011 2012 2013

Routine fundLoans

Government investment

0

20

40

60

80

100

()

Figure 3 Diagrams of investment scale and structure of scientificresearch funds

SampT and marine economy The empirical results show thatmarine scientific and technological research projects marinescientific and technological patents granted and researchfunds receipts of the marine scientific research institutionshave greater correlations with GOP which indicates that theyhave more impact on Chinarsquos marine economy

Therefore China needs to develop marine SampT espe-cially in research projects patents and research funds topromote marine economy and so as to make the economymore prosperous We need to further refine the NationalMarine EconomyDevelopment Plan to realize the sustainabledevelopment of marine economy in China and build Chinainto a maritime power

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The relevant researches done in this paper are supported bythe National Social Science FundMajor Projects (14ZDB151)General Financial Grant from theChina Postdoctoral ScienceFoundation (2015M580611) Qingdao Postdoctoral Appli-cation Research Project Funding (251) and FundamentalResearch Funds for the Central Universities (201613006201564031)

References

[1] J L Deng ldquoIntroduction to grey system theoryrdquoThe Journal ofGrey System vol 1 no 1 pp 1ndash24 1989

[2] L A Zadeh ldquoFuzzy algorithmsrdquo Information amp Control vol 12no 2 pp 94ndash102 1968

[3] Z Pawlak ldquoRough setsrdquo International Journal of Computer ampInformation Sciences vol 11 no 5 pp 341ndash356 1982

[4] P Liu L He and X Yu ldquoGeneralized hybrid aggregation opera-tors based on the 2-dimension uncertain linguistic informationfor multiple attribute group decision makingrdquo Group Decisionand Negotiation vol 25 no 1 pp 103ndash126 2016

[5] PD Liu Y Li and J Antucheviciene ldquoAmulti-criteria decision-making method based on intuitionistic trapezoidal fuzzy prior-itizedOWAoperatorrdquoTechnological and EconomicDevelopmentof Economy vol 22 no 3 pp 453ndash469 2016

[6] P Liu ldquoSome generalized dependent aggregation operators withintuitionistic linguistic numbers and their application to groupdecisionmakingrdquo Journal of Computer and System Sciences vol79 no 1 pp 131ndash143 2013

[7] P Liu and F Jin ldquoA multi-attribute group decision-makingmethod based on weighted geometric aggregation operators ofinterval-valued trapezoidal fuzzy numbersrdquoAppliedMathemat-ical Modelling vol 36 no 6 pp 2498ndash2509 2012

[8] P Liu X Zhang and F Jin ldquoA multi-attribute group decision-making method based on interval-valued trapezoidal fuzzynumbers hybrid harmonic averaging operatorsrdquo Journal ofIntelligent and Fuzzy Systems vol 23 no 5 pp 159ndash168 2012

[9] P Liu ldquoSome geometric aggregation operators based on intervalintuitionistic uncertain linguistic variables and their applicationto group decision makingrdquo Applied Mathematical Modellingvol 37 no 4 pp 2430ndash2444 2013

[10] J L Deng ldquoRelational space of grey theoryrdquo FuzzyMathematicsvol 4 no 2 pp 1ndash10 1985

[11] Z G Mei ldquoThe concept and computation method of greyabsolute correlation degreerdquo System Engineering no 05 pp 43ndash44 1992

[12] S F Liu Y G Dang Z G Fang et al Grey System Theory andApplication Science Press Beijing China 2012

[13] W X Tang ldquoThe concept and the computation method of Trsquoscorrelation degreerdquo Application of Statistics and Managementno 01 pp 34ndash37 1995

[14] Y G Dang ldquoResearch on grey relational analysis of sloperdquoSystem Sciences and Comprehensive Studies in Agriculture vol10 pp 331ndash337 1994

[15] Z L Wang and Q Y Wang ldquoSome properties of Grey B-relateddegreerdquo Journal of Hebei Mining and Civil Engineering Instituteno 3 pp 48ndash50 1992

[16] X H Zhao andQ YWang ldquoThe relational analysis of C-moderdquoJournal of Huazhong University of Science and Technology vol27 no 3 pp 75ndash77 1999

8 Mathematical Problems in Engineering

[17] H X Shi S F Liu Z G Fang et al ldquoThe model of greyperiodic incidence and their rehabilitationrdquo Chinese Journal ofManagement Science vol 3 pp 131ndash136 2008

[18] H Y Du H X Shi S F Liu et al ldquoStudy on the model ofgrey periodic incidence judged on sloperdquo Chinese Journal ofManagement Science no 01 pp 128ndash132 2010

[19] H J Xiong M Y Chen and T Qu ldquoSome extensions of greyrelational grade formulardquo Systems Engineering and Electronicsno 1 pp 8ndash10 2000

[20] Y G Dang S F Liu B Liu et al ldquoImprovement on degree ofgrey slope incidencerdquo Engineering Science vol 6 no 3 pp 41ndash44 2004

[21] Y G Sun and Y G Dang ldquoImproved model of slope greyrelational analysisrdquo Statistics and Decision no 15 pp 12ndash132007

[22] Y-G Sun and Y-G Dang ldquoImprovement on grey Trsquos correla-tion degreerdquo SystemEngineeringTheory and Practice vol 28 no4 pp 135ndash139 2008

[23] K Zhang and S-F Liu ldquoExtended clusters of grey incidencesfor panel data and its applicationrdquo System Engineering-Theory ampPractice vol 30 no 7 pp 1253ndash1259 2010

[24] X Li K W Hipel and Y Dang ldquoAn improved grey relationalanalysis approach for panel data clusteringrdquoExpert SystemswithApplications vol 42 no 23 pp 9105ndash9116 2015

[25] Y Wang X Shi J Sun and W Qian ldquoA grey interval relationaldegree-based dynamic multiattribute decision making methodand its application in investment decision makingrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 607016 6pages 2014

[26] Z Li G Wen and N Xie ldquoAn approach to fuzzy soft setsin decision making based on grey relational analysis andDempster-Shafer theory of evidence an application in medicaldiagnosisrdquo Artificial Intelligence in Medicine vol 64 no 3 pp161ndash171 2015

[27] S H Hashemi A Karimi and M Tavana ldquoAn integratedgreen supplier selection approachwith analytic network processand improved Grey relational analysisrdquo International Journal ofProduction Economics vol 159 pp 178ndash191 2015

[28] F L Wu F S Liu G L Yao et al ldquoFractional order greyrelational analysis and its applicationrdquo Scientia Iranica vol 22no 3 pp 1171ndash1178 2015

[29] X Guo Y Ni and Wangjia ldquoA grey relational analysis modelof scientific research ability on music based on AHP and itsrealizationrdquo International Journal of Signal Processing ImageProcessing amp Pattern Recognition vol 8 no 5 pp 211ndash222 2015

[30] G-W Wei ldquoGray relational analysis method for intuitionisticfuzzy multiple attribute decision makingrdquo Expert Systems withApplications vol 38 no 9 pp 11671ndash11677 2011

[31] X M Li Y G Dang and L Jin ldquoGrey trend analysis based ongrey relational degree with rate of change and its applicationrdquoChinese Journal of Management Science vol 23 no 9 pp 132ndash138 2015

[32] X Li Y Dang L Jin andWKang ldquoGCRAmodel for grey trendanalysis and its applicationrdquo Journal of Grey System vol 27 no1 pp 57ndash69 2015

[33] X M Li Y G Dang S Ding and J Zhang ldquoGrey accumula-tion generation relational analysis model for nonequidistanceunequal-length sequences and its applicationrdquo MathematicalProblems in Engineering vol 2014 Article ID 764857 8 pages2014

[34] G Q HuangW B Zhao and S H Xu ldquoA combinationmethodof improved grey relational degree and AHP for effectivenessevaluationrdquo in Proceedings of the 3rd International Conferenceon Mechatronics and Information Technology 2016

[35] X L Ning W U Ying-Xia Y U Tian-Peng et al ldquoResearchon comprehensive validation of simulation models based onimproved grey relational analysisrdquo Systems Engineering amp Elec-tronics vol 32 no 8 pp 1677ndash1679 2016

[36] N Xie Y Han and Z Li ldquoA novel approach to fuzzy soft sets indecision making based on grey relational analysis and MYCINcertainty factorrdquo International Journal of Computational Intelli-gence Systems vol 8 no 5 pp 959ndash976 2015

[37] W Wu and Y Peng ldquoExtension of grey relational analysis forfacilitating group consensus to oil spill emergency manage-mentrdquo Annals of Operations Research vol 238 no 1-2 pp 615ndash635 2016

[38] K Guo and Q Zhang ldquoDetecting communities in socialnetworks by local affinity propagation with grey relationalanalysisrdquo Grey Systems Theory and Application vol 5 no 1 pp31ndash40 2015

[39] X Liu and T Liu ldquoBlasting parameters optimization based ongrey relational analysisrdquo Gansu Metallurgy no 2 pp 1ndash3 2016

[40] NWang S X Zhang and J Cao ldquoApplication ofGrey relationalanalysis in evaluation of cross-fault deformation anomaly inter-ference factorsrdquo Journal of Seismological Research vol 38 no 1pp 90ndash98 2012

[41] J Qiao and J Zhu ldquoGovernment input to ocean science andtechnology and marine economic growth empirical studybased on panel datardquo Science and Technology ManagementResearch no 4 pp 37ndash40 2012

[42] B Dai G Jin and M Han ldquoAnalysis on temporal and spatialevolution of marine science and technology total factor pro-ductivity and its influencing factors in Chinese coastal areasrdquoGeographical Research vol 34 no 2 pp 328ndash340 2015

[43] R X Zhai and S O Business ldquoMarine science and technologyinvestment and marine economic growth an empirical studywith panel data in Chinarsquos coastal regionsrdquo Mathematics inPractice ampTheory no 4 pp 75ndash80 2014

[44] X X Zhang P F Zhang and X U Zi-Yi ldquoThe couplingevaluation model of Chinarsquos marine industrial aggregation andmarine science and technology talents aggregationrdquo Journal ofShandong University no 6 pp 118ndash128 2014

[45] D Liu X Li C Wang et al ldquoCalculating and forecasting ofmarine science and technology transfer raterdquoMarine Economyvol 5 no 2 pp 18ndash22 2015

[46] P Zhang X-R Li J-Y Zhang and Z-L Zhang ldquoIncludedangle distance of time series and similarity searchrdquo PatternRecognition and Artificial Intelligence vol 21 no 6 pp 763ndash7672008

[47] Y W Ding X H Yang A J Kavs et al ldquoSimilarity measure oftime series based on radian distancerdquo Journal of Electronics andInformation no 1 pp 122ndash128 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

8 Mathematical Problems in Engineering

[17] H X Shi S F Liu Z G Fang et al ldquoThe model of greyperiodic incidence and their rehabilitationrdquo Chinese Journal ofManagement Science vol 3 pp 131ndash136 2008

[18] H Y Du H X Shi S F Liu et al ldquoStudy on the model ofgrey periodic incidence judged on sloperdquo Chinese Journal ofManagement Science no 01 pp 128ndash132 2010

[19] H J Xiong M Y Chen and T Qu ldquoSome extensions of greyrelational grade formulardquo Systems Engineering and Electronicsno 1 pp 8ndash10 2000

[20] Y G Dang S F Liu B Liu et al ldquoImprovement on degree ofgrey slope incidencerdquo Engineering Science vol 6 no 3 pp 41ndash44 2004

[21] Y G Sun and Y G Dang ldquoImproved model of slope greyrelational analysisrdquo Statistics and Decision no 15 pp 12ndash132007

[22] Y-G Sun and Y-G Dang ldquoImprovement on grey Trsquos correla-tion degreerdquo SystemEngineeringTheory and Practice vol 28 no4 pp 135ndash139 2008

[23] K Zhang and S-F Liu ldquoExtended clusters of grey incidencesfor panel data and its applicationrdquo System Engineering-Theory ampPractice vol 30 no 7 pp 1253ndash1259 2010

[24] X Li K W Hipel and Y Dang ldquoAn improved grey relationalanalysis approach for panel data clusteringrdquoExpert SystemswithApplications vol 42 no 23 pp 9105ndash9116 2015

[25] Y Wang X Shi J Sun and W Qian ldquoA grey interval relationaldegree-based dynamic multiattribute decision making methodand its application in investment decision makingrdquoMathemat-ical Problems in Engineering vol 2014 Article ID 607016 6pages 2014

[26] Z Li G Wen and N Xie ldquoAn approach to fuzzy soft setsin decision making based on grey relational analysis andDempster-Shafer theory of evidence an application in medicaldiagnosisrdquo Artificial Intelligence in Medicine vol 64 no 3 pp161ndash171 2015

[27] S H Hashemi A Karimi and M Tavana ldquoAn integratedgreen supplier selection approachwith analytic network processand improved Grey relational analysisrdquo International Journal ofProduction Economics vol 159 pp 178ndash191 2015

[28] F L Wu F S Liu G L Yao et al ldquoFractional order greyrelational analysis and its applicationrdquo Scientia Iranica vol 22no 3 pp 1171ndash1178 2015

[29] X Guo Y Ni and Wangjia ldquoA grey relational analysis modelof scientific research ability on music based on AHP and itsrealizationrdquo International Journal of Signal Processing ImageProcessing amp Pattern Recognition vol 8 no 5 pp 211ndash222 2015

[30] G-W Wei ldquoGray relational analysis method for intuitionisticfuzzy multiple attribute decision makingrdquo Expert Systems withApplications vol 38 no 9 pp 11671ndash11677 2011

[31] X M Li Y G Dang and L Jin ldquoGrey trend analysis based ongrey relational degree with rate of change and its applicationrdquoChinese Journal of Management Science vol 23 no 9 pp 132ndash138 2015

[32] X Li Y Dang L Jin andWKang ldquoGCRAmodel for grey trendanalysis and its applicationrdquo Journal of Grey System vol 27 no1 pp 57ndash69 2015

[33] X M Li Y G Dang S Ding and J Zhang ldquoGrey accumula-tion generation relational analysis model for nonequidistanceunequal-length sequences and its applicationrdquo MathematicalProblems in Engineering vol 2014 Article ID 764857 8 pages2014

[34] G Q HuangW B Zhao and S H Xu ldquoA combinationmethodof improved grey relational degree and AHP for effectivenessevaluationrdquo in Proceedings of the 3rd International Conferenceon Mechatronics and Information Technology 2016

[35] X L Ning W U Ying-Xia Y U Tian-Peng et al ldquoResearchon comprehensive validation of simulation models based onimproved grey relational analysisrdquo Systems Engineering amp Elec-tronics vol 32 no 8 pp 1677ndash1679 2016

[36] N Xie Y Han and Z Li ldquoA novel approach to fuzzy soft sets indecision making based on grey relational analysis and MYCINcertainty factorrdquo International Journal of Computational Intelli-gence Systems vol 8 no 5 pp 959ndash976 2015

[37] W Wu and Y Peng ldquoExtension of grey relational analysis forfacilitating group consensus to oil spill emergency manage-mentrdquo Annals of Operations Research vol 238 no 1-2 pp 615ndash635 2016

[38] K Guo and Q Zhang ldquoDetecting communities in socialnetworks by local affinity propagation with grey relationalanalysisrdquo Grey Systems Theory and Application vol 5 no 1 pp31ndash40 2015

[39] X Liu and T Liu ldquoBlasting parameters optimization based ongrey relational analysisrdquo Gansu Metallurgy no 2 pp 1ndash3 2016

[40] NWang S X Zhang and J Cao ldquoApplication ofGrey relationalanalysis in evaluation of cross-fault deformation anomaly inter-ference factorsrdquo Journal of Seismological Research vol 38 no 1pp 90ndash98 2012

[41] J Qiao and J Zhu ldquoGovernment input to ocean science andtechnology and marine economic growth empirical studybased on panel datardquo Science and Technology ManagementResearch no 4 pp 37ndash40 2012

[42] B Dai G Jin and M Han ldquoAnalysis on temporal and spatialevolution of marine science and technology total factor pro-ductivity and its influencing factors in Chinese coastal areasrdquoGeographical Research vol 34 no 2 pp 328ndash340 2015

[43] R X Zhai and S O Business ldquoMarine science and technologyinvestment and marine economic growth an empirical studywith panel data in Chinarsquos coastal regionsrdquo Mathematics inPractice ampTheory no 4 pp 75ndash80 2014

[44] X X Zhang P F Zhang and X U Zi-Yi ldquoThe couplingevaluation model of Chinarsquos marine industrial aggregation andmarine science and technology talents aggregationrdquo Journal ofShandong University no 6 pp 118ndash128 2014

[45] D Liu X Li C Wang et al ldquoCalculating and forecasting ofmarine science and technology transfer raterdquoMarine Economyvol 5 no 2 pp 18ndash22 2015

[46] P Zhang X-R Li J-Y Zhang and Z-L Zhang ldquoIncludedangle distance of time series and similarity searchrdquo PatternRecognition and Artificial Intelligence vol 21 no 6 pp 763ndash7672008

[47] Y W Ding X H Yang A J Kavs et al ldquoSimilarity measure oftime series based on radian distancerdquo Journal of Electronics andInformation no 1 pp 122ndash128 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of