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Advances in Fuzzy Mathematics.
ISSN 0973-533X Volume 12, Number 3 (2017), pp. 677-692
© Research India Publications
http://www.ripublication.com
Document Classification for Large Datasets Based On
Hesitant Fuzzy Linguistic Term Set
Swatantra Kumar Sahu 1, Bharat Mishra2 and R. S. Thakur3
1 M.G.C.G.V.V., Satna, Madhya Pradesh, India.
2 M.G.C.G.V.V., Satna, Madhya Pradesh, India. 3 MANIT, Bhopal, Madhya Pradesh, India.
Abstract
This paper presents Hesitant Fuzzy information about large data sets. Hesitant
Fuzzy Linguistic Term Set (HFLTS) is based on the fuzzy linguistic approach
that will serve as basis to Increase the flexibility of elicitation of linguistic
Information. Experimental results evaluated using the Analytical Tool
MATLAB 7.14. The classification results show the proposed approach
performs well.
Keywords: Hesitant Fuzzy Set, Classification, Large Data sets, Linguistic
Term Set.
1. INTRODUCTION
Hesitant Fuzzy Information collection is refer Fuzzy logic, Fuzzy sets theory,
Intuitionistic fuzzy sets, Fuzzy multi sets, fuzzy linguistic approach, uncertainty and
loading of data etc. In this Paper Hesitant Fuzzy Linguistic Term Set (HFLTS) is used
to classify the document datasets.
Fig 1: Hesitant Fuzzy Information collection
Hesitant Fuzzy set
Linguistic Term Set Dual S et
678 Swatantra Kumar Sahu, Bharat Mishra and R.S. Thakur
In the area of document classification various approach proposed by researcher some
of listed blow Swatantra Kumar Sahu, et.al.“Hesitant Fuzzy Linguistic Term Set
Based Document Classification”[48], S.A. Orlovsky, “Decision-making with a fuzzy
preference relation[25], Swatantra Kumar Sahu, et.al “Numerical Result Analysis of
Document Classification for Large Data Sets” [49],H. Becker, “Computing with
words and machine learning in medical diagnosis[2],Y.Dong,et.al.“Computing the
numerical scale of the linguistic term set for the 2-tuple fuzzy linguistic representation
model [5].
L. Martinez, et.al. “Computing with words in decision support systems: An overview
on models and applications [21], D.Dubois, et.al. Fuzzy Sets and Systems: Theory
and Applications [6]. Z. P. Fan, et.al. “An approach to multiple attribute decision
making based on fuzzy preference information alternatives [7], D. F. Li,“TOPSIS-
based nonlinear-programming methodology for multi attribute decision making with
interval-valued intuitionistic fuzzy sets[18].
F. Herrera, et.al. “A fusion approach for managing multi-granularity linguistic terms
sets in decision making[10], F. Herrera et.al. “A 2-tuple fuzzy linguistic
representation model for computing with words[12]S. Kundu, “Min-transitivity of
fuzzy leftness relationship and its application to decision making [16], H. Ishibuchi
et.al. “Theory and methodology: Multi objective programming in optimization of the
interval objective function [14].
G. Bordogna et.al. “A fuzzy linguistic approach generalizing Boolean information
retrieval: A model and its evaluation [4], J. Kacprzyk et.al. “Computing with words is
an implementable paradigm: Fuzzy queries, linguistic data summaries, and natural-
language generation[15].
H. Ishibuchi, et.al. , Classification and Modelling With Linguistic Information
Granules: Advanced Approaches to Linguistic Data Mining [13],D. F. Li, “Multi
attribute group decision making method using extended linguistic variables[17].
P. P. Bonissone, “A fuzzy sets based linguistic approach: Theory and applications
[3],J. Ma, et.al., “A fuzzy-set approach to treat determinacy and consistency of
linguistic terms in multi-criteria decision making[19], F. Herrera, E. Herrera-Viedma,
et.al., “A fuzzy linguistic methodology to deal with unbalanced linguistic term
sets[11], L. Mart´ınez, “Sensory evaluation based on linguistic decision analysis[20].
J. M. Mendel, “An architecture for making judgement using computing with
words[22],K.T. Atanassov, “Intuitionistic fuzzy sets[1], J.M. Mendel, et.al.,“What
computing with words means to me[23], M. Mizumoto et.al., “Some properties of
fuzzy sets of type 2[24], Rosa M. Rodr´ıguez, et.al., “Hesitant Fuzzy Linguistic Term
Sets for Decision Making”[44].J.M. Garibaldi, et.al., “Nonstationary fuzzy sets [8].
W. Pedrycz et.al., “Analytic hierarchy process (AHP) in group decision making and
its optimization with an allocation of information granularity [27], F. Herrera, et.al.,
“Computing with words in decision making: Foundations, trends and prospects[9] ,
M. Roubens, “Some properties of choice functions based on valued binary
Document Classification for Large Datasets Based On Hesitant Fuzzy… 679
relations[28].
V.Torra, “Negation function based semantics for ordered linguistic labels[31], R. R.
Yager, “On the theory of bags[37],V. Torra, “Hesitant fuzzy sets[32], Y. Tang et.al.
“Linguistic modelling based on semantic similarity relation among linguistic
labels[30], I. B. T¨urks¸en, “Type 2 representation and reasoning for CWW[33].
Y. M.Wang, J et.al., “A preference aggregation method through the estimation of
utility intervals [35], L. A. Zadeh, “The concept of a linguistic variable and its
applications to approximate reasoning—Part I[40].
D.Wu et.al., “Computing with words for hierarchical decision making applied to
evaluating a weapon system [36], A. Sengupta et.al., “On comparing interval numbers
[29].
R. R. Yager, “An approach to ordinal decision making [38], J. H. Wang et.al., “A new
version of 2-tuple fuzzy linguistic representation model for computing with words
[34], L. A. Zadeh, “The concept of a linguistic variable and its applications to
approximate reasoning—Part II[41] L. A. Zadeh, “Fuzzy sets[39]. L. A. Zadeh, “The
concept of a linguistic variable and its applications to approximate reasoning—Part
III[42].
S. M. Zhou, R et.al., “On aggregating uncertain information by type-2 OWA
operators for soft decision-making[43],S. Parsons, “Current approaches to handling
imperfect information in data and knowledge bases[26],Hesitant Distance Similarity
Measures for Document Clustering[45].
Hesitant k-Nearest Neighbor (HK-nn) Classifier for Document Classification and
Numerical Result Analysis[47], Computing Vectors Based Document Clustering and
Numerical Result Analysis[46].
This paper is organized as follows. Section-1 described the introduction and review of
literatures. In Section-2, the Hesitant Fuzzy Information is described. In Section-3,
Methodology of document Classification is described. In Section-4, Experimental
results are described. Finally, we concluded and proposed some future directions in
Conclusion Section, i.e. Section 5.
2 HESITANT FUZZY LINGUISTIC TERM SET
Uncertainty problem is occurs during calculation of document classification results,
for handling this problem the best and optimum solution is Hesitant Fuzzy Set.
Hesitant Fuzzy Set gives new computational solution with numerical capability.
Hesitant Fuzzy used Linguistic Term Set it knows Hesitant Fuzzy Linguistic Term Set
(HFLTS). Linguistic Term Set just like Context Free Grammar (CFG) [44].
Definition 1: Let S be a linguistic term set, S={S0,-----,Sg}, an HFLTS, Hs, is an
ordered finite subset of the consecutive linguistic terms of S. and define the empty
HFLTS and the full HFLTS for a linguistic variable λ as follows.
680 Swatantra Kumar Sahu, Bharat Mishra and R.S. Thakur
1) Empty HFLTS: Hs(λ)={}
2) Full HFLTS: Hs(λ)=S.
Any other HFLTS is formed with at least one linguistic term in S.
Example 1: Let S be a linguistic term set S={ S0:nothing, S1:verylow,S2:low,S3 :
medium, S4:high,S5:veryhigh,S6:perfect} a different HFLTS might be
Hs(λ)={ S1 :very low, S2 :low, S3 : medium }
Hs(λ)={ S3 :medium, S4: high, S5:veryhigh, S6:perfect }
Once the concept of HFLTS has been defined, it is necessary to introduce the
computation and operations that can be performed on them.
Let S be a linguistic term set, S= {S0,-----,Sg},and Hs , Hs1 ,Hs2 be the three HFLTS.
Definition 2: The upper bound Hs+ and lower bound Hs- of the HFLTS, Hs are
defined as
1) Hs+ =max(si )=sj , si Hs, si ≤ sj for all i
2) Hs- =min(si )=sj , si Hs, si ≤ sj for all i
Definition 3: The complement of HFLTS Hs, is defined as
Hs = S - Hs ={ si / si S, si Hs }.
Definition 4: The envelope of the HFLTS env(Hs), is a linguistic interval whose
limits are obtained by means of upper bound (max) and lower bound (min). Hence
env(Hs)=[ Hs- ,Hs+]
Example2: Let S={ S0:nothing, S1 :very low, S2 :low, S3 :medium,
S4:high,S5:veryhigh,S6:perfect}be a linguistic term set, and Hs={ high,very
high,perfect } be an HFLTS of S, its envelope is
Hs- ={ high,very high,perfect }=high
Hs+ ={ high,very high,perfect }=perfect
env(Hs)=[ high , perfect] .
Document Classification for Large Datasets Based On Hesitant Fuzzy… 681
Table 1: Hesitant Fuzzy Linguistic Term Set (HFLTS)
Data
Set
S={ S0:nothing,
S1 :very low, S2 :low, S3:medium,
S4:high, S5:veryhigh, S6:perfect}
Hs+ ={ high, very
high, perfect
}=perfect
Hs- ={ high, very
high, perfect }=high
env(Hs)=[
high ,
perfect]
D1 {0,2,3,5,7,9,6} {7,9,6 }=6 {7,9,6 }=7 {7,6}
D2 {0,4,7,9,13,15,12} {13,15,12}=12 {13,15,12}=13 {13,12)
D3 {0,1,3,6,8,10,7} {8,10,7}=7 {8,10,7}=8 {8,7}
D4 {0,6,11,17,22,29,19} {22,29,19}=19 {22,29,19}=22 {22,19}
D5 {0,3,7,8,12,13,11 } {12,13,11}=11 {12,13,11}=12 {12,11}
D6 {0,9,24,29,35,40,33} {35,40,33}=33 {35,40,33}=35 {35,33}
D7 {0,7,11,16,22,27,21} {22,27,21 }=21 {22,27,21 }=22 {22,21}
D8 {0,5,9,14,17,23,16 } {17,23,16}=16 {17,23,16}=17 {17,16}
Table 2: Accuracy (in %) with Bag of Words Datasets ,20-news group Datasets and
Legal Case Reports Datasets
Bag of Word 20 News Group Le
gal
Case Report
No. of
Data Set
K-
NN
HFLTS Centroid SVM K-
NN
HFLTS Centroid SVM K-
NN
HFLTS Centroid SVM
50 0.84 0.97 0.87 0.89 0.83 0.93 0.87 0.80 0.81 0.91 0.82 0.85
100 0.86 0.94 0.86 0.71 0.82 0.94 0.83 0.71 0.82 0.92 0.83 0.76
200 0.82 0.92 0.85 0.73 0.81 0.96 0.85 0.83 0.82 0.93 0.84 0.85
350 0.80 0.93 0.79 0.76 0.90 0.91 0.73 0.86 0.90 0.91 0.78 0.84
500 0.77 0.89 0.73 0.78 0.84 0.89 0.73 0.78 0.83 0.89 0.78 0.78
650 0.78 0.88 0.76 0.79 0.75 0.83 0.75 0.79 0.72 0.82 0.78 0.74
800 0.73 0.86 0.72 0.72 0.73 0.96 0.72 0.82 0.73 0.92 0.77 0.82
1000 0.76 0.83 0.71 0.71 0.76 0.93 0.70 0.71 0.67 0.92 0.70 0.71
Table 3: F-measure value with Bag of Words datasets, 20-news group Datasets and
Legal Case Reports Datasets
Bag of Word 20 News Group Le
gal
Case Report
No. of
Data
Set
K-
NN
HFLTS Centroid SVM K-
NN
HFLTS Centroid SVM K-
NN
HFLTS Centroid SVM
5 0.82 0.97 0.86 0.88 0.81 0.92 0.86 0.88 0.81 0.96 0.86 0.84
10 0.83 0.94 0.87 0.72 0.84 0.94 0.77 0.77 0.84 0.95 0.85 0.72
20 0.82 0.92 0.84 0.73 0.82 0.92 0.84 0.73 0.83 0.96 0.84 0.76
35 0.83 0.93 0.80 0.72 0.82 0.93 0.70 0.77 0.86 0.93 0.86 0.72
50 0.87 0.89 0.74 0.78 0.87 0.92 0.74 0.78 0.87 0.88 0.74 0.75
682 Swatantra Kumar Sahu, Bharat Mishra and R.S. Thakur
65 0.88 0.92 0.77 0.72 0.88 0.92 0.77 0.77 0.88 0.98 0.75 0.72
80 0.83 0.86 0.71 0.72 0.82 0.96 0.71 0.72 0.84 0.88 0.71 0.75
100 0.56 0.83 0.72 0.74 0.56 0.93 0.72 0.74 0.56 0.84 0.75 0.74
3. METHODOLOGY:
In Classification of document, different steps are used. The steps are shown in fig 2.
Fig 2: Hesitant Fuzzy Linguistic Term Set
4 EXPERIMENTAL RESULTS
In this Experiment we calculate Hesitant Fuzzy Linguistic Term Set (HFLTS) in
Document dataset. Document Classification upper bound Hs+, envelope of the
HFLTS and lower bound Hs- of the HFLTS HS are calculated which describe in Table
1 and Table 2 respectively. Table 3 to Table 5 describes classification accuracy for
Bag of Words, 20-news group and Legal Case Reports Datasets respectively. Table 6
to Table 8 describes F-measure values for Bag of Words, 20-news group and Legal
Case Reports Datasets respectively.
This Experiment shows, Hesitant Fuzzy Linguistic Term Set (HFLTS) based
Document Classification is efficient and accurate compare to other Document
Classification. From Fig.2 to Fig. 9, Hesitant Fuzzy Linguistic Term Set is described.
Data
Collection
Data Preprocessing
Calculations of HFLTS
Calculations of Hs+ and Hs- Determine the envelope Classification Results
Document Classification for Large Datasets Based On Hesitant Fuzzy… 683
From Fig. 10 to Fig.11, Upper bound Hs+ , lower bound Hs- of the HFLTS are
described respectively.
Fig. 12 to Fig.14 describes classification accuracy results for Bag of Words, 20-news
group and Legal Case Reports Datasets respectively. Fig. 15 to Fig.17 describes F-
measure values for Bag of Words, 20-news group and Legal Case Reports Datasets
respectively.
D1H+ upper bound, D1H- lower bound are dataset 1, D2H+ upper bound, D2H- lower
bound are dataset 2, D3H+ upper bound, D3H- lower bound are dataset 3, D4H+ upper
bound, D4H- lower bound are dataset 4 , D5H+ upper bound, D5H- lower bound are
dataset 5, D6H+ upper bound, D6H- lower bound are Dataset 6, D7H+ upper bound,
D7H- lower bound are dataset 7, D8H+ upper bound, D8H- lower bound are dataset 8
in graphical representation of Fig.2 to Fig.9 respectively.
Fig 2: Hesitant Fuzzy Linguistic Term Set
Fig 3: Hesitant Fuzzy Linguistic Term Set
02468
10
Dat
a S
et 1
HFLTS
Data
05
101520
Dat
a S
et 2
HFLTS
Data
684 Swatantra Kumar Sahu, Bharat Mishra and R.S. Thakur
Fig 4: Hesitant Fuzzy Linguistic Term Set
Fig 5: Hesitant Fuzzy Linguistic Term Set
Fig 6: Hesitant Fuzzy Linguistic Term Set
02468
1012
Dat
a S
et 3
HFLTS
Data
05
101520253035
Dat
a S
et
4
HFLTS
Data
0
5
10
15
Dat
a S
et
5
HFLTS
Data
Document Classification for Large Datasets Based On Hesitant Fuzzy… 685
Fig 7: Hesitant Fuzzy Linguistic Term Set
Fig 8: Hesitant Fuzzy Linguistic Term Set
Fig 9: Hesitant Fuzzy Linguistic Term Set
0
10
20
30
40
50
Dat
a S
et
6
HFLTS
Data
0
5
10
15
20
25
30
Dat
a S
et 7
HFLTS
Data
05
10152025
Dat
a S
et 8
HFLTS
Data
686 Swatantra Kumar Sahu, Bharat Mishra and R.S. Thakur
Fig 10: Hesitant Fuzzy Linguistic Term Set
Fig 11: Hesitant Fuzzy Linguistic Term Set
Fig 12: Accuracy for Bag of Words datasets
0
5
10
15
20
25
Dat
a S
et 1
,2,3
,4
HFLTS
Data
0
5
10
15
20
25
30
35
40
Dat
a S
et 5
,6,7
,8
HFLTS
Data
0
0.2
0.4
0.6
0.8
1
1.2
50 100 200 350 500 650 800 1000
Acc
ura
cy %
Number of Clusters
Bag of Words Datasets
K-NN
HFLTS
centroid
SVM
Document Classification for Large Datasets Based On Hesitant Fuzzy… 687
Fig 13: Accuracy for 20-news group datasets
Fig 14: Accuracy for Legal Case Reports Datasets
Fig 15: F-measure for Bag of Words datasets
0
0.5
1
1.5
20
-ne
ws
gro
up
Dat
ase
ts f
or
Acc
ura
cy %
Number of Clusters
20-news group Datasets
K-NN
HFLTS
centroid
SVM
0
0.5
1
1.5
Lega
l Cas
e R
ep
ort
s D
atas
ets
fo
r A
ccu
racy
%
Number of Clusters
Legal Case Reports Datasets
K-NN
HFLTS
Centroid
SVM
0
0.2
0.4
0.6
0.8
1
1.2
5 10 20 35 50 65 80 100Over
all
F-m
easu
re
Number of Clusters
Bag of Words Datasets
K-NN
HFLTS
Centroid
SVM
688 Swatantra Kumar Sahu, Bharat Mishra and R.S. Thakur
Fig 16: F-measure from 20-news group Datasets
Fig 17: F-measure from Legal Case Reports Datasets
5. CONCLUSION:
As result & analysis shows that The Document Classification based on Hesitant Fuzzy
Linguistic Term Set is efficient and the HFLTS classification has the potential to
improve the classification accuracy.
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