�

Abstract²The paper aims to quantify the phenomenon of

domestic violence, which based on the gender statistics from

7DLZDQ¶V� JRYHUQPHQW, and use GM (0,N) model as the

mathematics model to analyze the problem of domestic violence

victims from year 2006 to year 2010. The paper proposes the ten

influence factors for the domestic violence at first. Through GM

(0,N) calculation, the result shows that the three main factors

influence domestic violence for male victims are the graduate

school, the self-study and university, while for female victims are

self-study, graduate school and illiterate.

I. INTRODUCTION

aiwan became the first country that enacted the

Domestic Violence Prevention Act in 1998. The Act

provides a mechanism for the public authority to

intervene the private segment and called µlaw applies to home

affairs¶ over ten years. However, domestic violence(DV)

cases happened continuously, and reported cases increased

consequently.

Related researches on domestic violence and sexuality,

education etc., for example, L.P. Kes¶ pointed out the rate of

male DV victims is 14.1% of all reported cases and female

victims is 85.9% in 2003 statistics data from the Ministry of

the Interior. Comparing child, marital, aged violence

protection etc. with that of 2002, most female victims are

marital DV victims while male victims are child and aged

violence victims>1@. Kaohsiung Police Agency pointed out the

rate of female victims is 82.7% of its all reported cases, while

male victims is 17.3%, and senior high school 38.8%, junior

high school 20.8%, primary school 15.3% from 2004 to 2010,

through discussing victims¶ sexuality, education,

occupation«of fifteen factors>2@. F.L. Chen pointed out the

rate of senior high school is 38.63%, junior high school

23.82%, primary school 19.42% in 2009 of her collected local

police agencies¶ DV case investigation records>3@.Those materials focused on the influence between different

factors and DV, and they lack of significant statistical

quantitative researches in the factor analysis of DV. This

Manuscript received September 8, 2012.

S. F. Chen is with the Chang Jung Christian University, Tainan,

Taiwan(e-mail:sfc@mail.cjcu.edu.tw).

M. C. Wei is with the General Education Department, Chienkuo

Technology University, Changhua, Taiwan (corresponding author phone:

886-958-216998; fax: 886-4-7111158; e-mail: meichan@cc.ctu.edu.tw).

W. H. Fang is with the General Education Department, Chienkuo

Technology University, Changhua, Taiwan (e-mail: whfang@cc.ctu.edu.tw).

M. H. Chen is with the General Education Department, Chienkuo

Technology University, Changhua, Taiwan (e-mail: hui0811.chen@msa.

hinet.net).

paper aims to quantify the education phenomenon of DV

based on the gender statistics from the Domestic Violence and

Sexual Assault Prevention Committee, the Ministry of the

Interior. The paper proposes the concrete factors of education

include preschool, self-study, illiterate, primary school, junior

high school, senior high school, junior college, university,

graduate school and unknown.

Hence, the paper uses the GM(0,N) in the grey system

theory, by using the calculation of GM(0,N) to understand the

domestic violence victims in Taiwan, and understand variables

associated with the greatest impact in overall women

development process in Taiwan. At the end, the status of

women could be improved.

In section II, the whole mathematical foundation of

GM(0,N) in grey system theory is presented. Section III,

present a real example in Taiwan. The final section of this

study consists of a conclusion and recommendations for future

research.

II. GM(0,N) MODEL

In grey system theory, the main function of GM(h,N) model

is one of the methods to carry out the calculation of

measurement among the discrete sequences and to

compensate the shortcomings in the traditional methodology.

If in sequences Nikxi ,,3,2,1,)()0( / , )(

)0(1 kx is the main

factor in the system, and sequences ),(,)(,)()0(

4)0(

3)0(

2 kxkxkx

)(,,)()0()0(

5 kxkx N/ are the influence factors, then, the GM(h,N)

model is defined as[4,5].

¦¦

N

j

jj

h

ii

i

i kxbtd

xda

2

)1(

0)(

)1(1

)(

)( (1)

where: i. 1a and jb are determined coefficients.

ii. )()1(1 kx : The major sequence.

iii. )()1( kx j : The influencing sequences.

iii. )1()0(AGO xx

¦¦¦

3

1

)0(2

1

)0(1

1

)0( ),(),(),([

kkk

kxkxkx ¦

n

k

kx

1

)0( )](...

The GM(0,N) model is the special topic in GM(h,N), and

the mathematics model is shown below.

¦

N

j

jj kxbkaz

2

)1()1(1 )()(

)()()()1()1(

33)1(

22 kxbkxbkxb NN��� / (2)

Apply GM(0,N) to Analyze the Weighting of Influence Factor in

Education to Domestic Violence Victim-An Example in Taiwan

Show-Feng Chen, Mei-Chuan Wei, Wen-Hui Fang and Mei-Hui Chen

T

2012 IEEE/SICE International Symposium on System Integration (SII)Kyushu University, Fukuoka, JapanDecember 16-18, 2012

978-1-4673-1497-8/12/$31.00 ©2012 IEEE 660

where: nkkxkxkz ,,4,3,2),(5.0)1(5.0)()1(

1)1(

1)1(

1 / ��

and the analysis steps are

1) Substituting the AGO value

)()()(

)4()4()4(

)3()3()3(

)2()2()2(

)1()1(22

)1(11

)1()1(22

)1(11

)1()1(22

)1(11

)1()1(22

)1(11

nxbnxbnza

xbxbza

xbxbza

xbxbza

NN

NN

NN

NN

��

��

��

��

/

//////////

/

/

/

(3)

2) Dividing 1a in both sides: Translate into matrix form

»»»»»»»»»»

¼

º

««««««««««

¬

ª

»»»»»

¼

º

«««««

¬

ª

»»»»»

¼

º

«««««

¬

ª

��

�

�

1

1

4

1

3

1

2

)1()1(2

)1()1(2

)1()1(2

)1(1

)1(1

)1(1

)1(1

)1(1

)1(1

)()(

)3()3(

)2()2(

)(5.0)1(5.0

)3(5.0)2(5.0

)2(5.0)1(5.0

a

b

a

b

a

b

a

b

nxnx

xx

xx

nxnx

xx

xx

N

N

N

N

0/

0/0

/

/

0

(4)

and assume m

jb

a

bÖ

1

, where ,,,4,3,2 Nm / then equation

(4) can be rearranged into

»»»»»»

¼

º

««««««

¬

ª

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¼

º

«««««

¬

ª

»»»»»

¼

º

«««««

¬

ª

��

�

�

NN

N

N

b

b

b

b

nxnx

xx

xx

nxnx

xx

xx

Ö

Ö

Ö

Ö

)()(

)3()3(

)2()2(

)(5.0)1(5.0

)3(5.0)2(5.0

)2(5.0)1(5.0

4

3

2

)1()1(2

)1()1(2

)1()1(2

)1(1

)1(1

)1(1

)1(1

)1(1

)1(1

0/

0/0

/

/

0

(5)

3) Use XYYYB TT 1)(Ö � to solve the values of mbÖ :

where:

»»»»»

¼

º

«««««

¬

ª

��

�

�

)(5.0)1(5.0

)3(5.0)2(5.0

)2(5.0)1(5.0

)1(1

)1(1

)1(1

)1(1

)1(1

)1(1

nxnx

xx

xx

X0

,

»»»»»

¼

º

«««««

¬

ª

)()(

)3()3(

)2()2(

)1()1(2

)1()1(2

)1()1(2

nxnx

xx

xx

Y

N

N

N

/

0/0

/

/

,

»»»»»»

¼

º

««««««

¬

ª

Nb

b

b

b

B

Ö

Ö

Ö

Ö

Ö4

3

2

0

the relationship between the major sequence and the

influencing sequences can be found by comparing the values

of mbÖ .

III. THE REAL EXAMPLE

The original source of the gender statistics is from the

Domestic Violence and Sexual Assault Prevention Committee,

the Ministry of the Interior, and the preliminary analysis

shows the preschool, self-study, illiterate, primary school,

junior high school, senior high school, junior college,

university, graduate school and unknown of either male or

female victims have shown significant growth in the number

of DV (see TABLE I). But the main impact factor among the

factors cannot be obtained [6]. Therefore, the paper collected

the statistic numbers, which can be affected to analyze the

impact factors to domestic violence victim

A. Analysis Indicators

According to statistical indicators of the content, each

factor is explained as follows.

1) Preschool: 0-6 years old child before primary school.

2) Self-study: One never studied in national education

system, but learned systematically by oneself.

3) Illiterate: One never studied in national education system,

and never learned systematically by oneself.

4) Primary school: One studied through the primary school

in national education system.

5) Junior high school: One studied through the junior high

school in national education system.

6) Senior high school: One studied through the senior high

school in national education system.

7) Junior college: One studied through the junior college in

national education system.

8) University: One studied through the university in national

education system.

9) Graduate school: One studied through the graduate

school in national education system.

10) Unknown: One¶s education situation did not show at

reported form.

B. Analysis steps

Based on TABLE I and TBALE II, the analysis steps are

listed below[7,8]

1) Building the analysis structure

The whole structure is shown in Fig. 1.

GM(0,N)

Preschool

Self-study

Illiterate

Primary school

OutputJunior high school

University

Junior college

Senior high school

2Öb

3Öb

4Öb

5Öb

6Öb

7Öb

8Öb

9Öb

Unknown11Öb

Graduate

university 10Öb

Fig. 1 The analysis structure

2) Building the original sequences(The male part)

661

According to the characteristic of GM(0,N), the

sequences of original are listed below)0(

1x =(11763, 14202, 16508, 18509, 22999)

)0(2x =(1537, 2088, 2454, 2432, 3000)

)0(3x =(26, 25, 42, 32, 35)

)0(4x =(335, 324, 279, 326, 312)

)0(5x =(3226, 3823, 4478, 4914, 5932)

)0(6x =(1843, 2299, 2750, 3012, 3820)

)0(7x =(1693, 2064, 2387, 2979, 3521)

)0(8x =(475, 532, 592, 753, 883)

)0(9x =(436, 506, 707, 873, 1118)

)0(10x =(130, 133, 184, 236, 290)

)0(11x =(2062, 2408, 2635, 2952, 4088)

3) Building the AGO sequences

Use AGO to build the sequences, as shown below)1(

1x =(11763, 25965, 42473, 60982, 83981)

)1(1z =(----,18864,34219, 51727.5, 72481.5)

)1(2x =(1537, 3625, 6079, 8511, 11511)

)1(3x =(26, 51, 93, 125, 160)

)1(4x =(335, 659, 938, 1264, 1576)

)1(5x =(3226, 7049, 11527, 16441, 22373)

)1(6x =(1843, 4142, 6892, 9904, 13724)

)1(7x =(1693, 3757, 6144, 9123, 12644)

)1(8x =(475, 1007, 1599, 2352, 3235)

)1(9x =(436, 942, 1649, 2522, 3640)

)0(10x =(130, 263, 447, 683, 973)

)0(11x =(2062, 4470, 7105, 10057, 14145)

4) Calculation

After the sequences are built, then, substitute into

equation (5) to find the weighting for each factor.

»»»»»»

¼

º

««««««

¬

ª

»»»»

¼

»

««««

¬

«

»»»»

¼

º

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¬

ª

11

4

3

2

Ö

Ö

Ö

Ö

1414516011511

100571258511

7105936079

4470513625

5.72481

5.51727

32419

1864

b

b

b

b

0/

0

/

/

and list the results in TABLE III. Same as the calculation

steps mentioned above, we can get the results about the

female, and also list in TABLE IV. In this research, we

use toolbox to verify our results, and shown in Fig. 2 and

Fig. 3[9].

Fig. 2 The verify by use toolbox-Male

Fig. 3 The verify by use toolbox-Female

IV. CONCLUSION

Through GM (0,N) calculation, the influence of education

factor to male and female DV victims is analyzed. The result

shows that the main factors influence the increasing number of

DV victims are the graduate school firstly, the self-study

secondly and the university thirdly for male victims, while the

self-study firstly, the graduate school secondly and the

illiterate thirdly for female victims. Although there are a little

different between male and female, the number of the graduate

school and the self-study of both male and female victims, and

male with university degree, illiterate female victims is not so

large, but their growth rate is very high. This is an obvious

phenomenon, and a helpful reference for adopting DV

prevention measures.

To sum up, the GM(0,N) that used in this study is one of the

software calculation methods. Therefore, in addition to

including other related influence factors,(e.g. occupation,

nationality etc� further studies can increase the amount of

data, in order to enhance validity. Furthermore, other soft

computing method, such as the fuzzy, ANN, and rough set

theory, can be integrated to the grey system theory enhance the

reliability of results.

662

ACKNOWLEDGMENT

The authors want to heartily thank Taiwan Kansei

Information Association to provide the toolbox in this

research.

REFERENCES

[1] L.P. Ke, P.L. Wang, C.L. Chang,� ³Domestic Violence: Theories and

Policy and Practice,´ Chuliu Publisher,Taipei, pp. 6-15, 2005.

[2] Kaohsiung City Police Agency, Kaohsiung Police Statistics on

Domestic Violence Prevention, 2010, http://www2. ohchr.org/

english/issues/poverty/docs/A.HRC.Sub.1.58.SF.3_.doc(visited

20120111).

[3] F.L. Chen- Sftfbsdi po Fggfdujwfoftt of Domestic Violence

Prevention Policy, commissioned research of Research, Development

and Evaluation Commission, Executive Yuan, p.66 ,2011.

[4] K. L. Wen, Grey systems modeling and prediction��<DQJ¶V�6FLHQWLILF�

Research Institute, USA, 2004.

[5] M. L. You, Y. Y. Lyu, J. R. Wang and K. L. Wen,�³$SSO\�*0�K�1��WR�

DQDO\]H� WKH� ZHLJKWLQJ� RI� LQIOXHQFH� IDFWRU� LQ� UHVRXUFH� UHF\FOLQJ�´� in

Proc. Conference on Information Technology and Applications in

Outlying Islands, 2011.

[6] Department of Statistics of Ministry, The statistic data of the Interior

in Taiwan, Department of Statistics of Ministry, Taiwan, 2011.

[7] K. L. Wen, Grey system theory and its application, Wunan Publisher,

Taipei, 2009.

[8] K. L. Wen, M. L. You, and J. 5��:DQJ��³7KH�development of Matlab

WRROER[� IRU� NDQVHL� IDFWRU� DQDO\VLV�´� International Journal of Kensei

Information, vol. 1, no. 1, pp. 43-52, 2010.

[9] M.C. Wei, M. H. Chen, W. H. Fang and H. C Huang �³Apply GM(0,N)

to Analyze the Weighting of Influence Factor in the Feminization of

Poverty-An Example in Taiwan´ in Conference IEEE/SICE

International Symposium on System Integration in Kyoto, 2011.

663

TABLE I

THE DATA FROM YEAR 2006 TO YEAR 2010 (MALE-PERSON)

Year Age 0-6 (x2) Self-Study (x3) Illiterate (x4) Primary School (x5)

2006 1,537 26 335 3,226

2007 2,088 25 324 3,823

2008 2,454 42 279 4,478

2009 2,432 32 326 4,914

2010 3,000 35 312 5,932

Year Junior High School (x6) Senior High School (x7) Junior College (x8) University (x9)

2006 1,843 1,693 475 436

2007 2,299 2,064 532 506

2008 2,750 2,387 592 707

2009 3,012 2,979 753 873

2010 3,820 3,521 883 1,118

Year Graduate School (x10) Unknown (x11) Output(x1)

2006 130 2,062 11,763

2007 133 2,408 14,202

2008 184 2,635 16,508

2009 236 2,952 18,509

2010 290 4,088 22,999

TABLE II

THE DATA FROM YEAR 2006 TO YEAR 2010 (FEMALE-PERSON)

Year Age 0-6 (x2) Self-sudy (x3) Illiterate (x4) Primary shool (x5)

2006 1,226 108 1,489 7,384

2007 1,670 107 1,432 7,716

2008 1,929 84 1,442 8,250

2009 1,997 100 1,551 8,755

2010 2,395 110 1,660 9,894

Year Junior high school (x6) Senior high school (x7) Junior college (x8) University (x9)

2006 9,050 14,805 3,555 2,483

2007 9,703 15,633 3,461 2,719

2008 9,971 16,162 3,765 3,199

2009 11,306 17,891 4,091 3,943

2010 12,440 19,356 4,384 4,720

Year Graduate school (x10) Unknown (x11) Output(x1)

2006 338 10,034 50,472

2007 386 9,946 52,773

2008 475 11,999 57,276

2009 580 13,509 63,723

2010 642 18,514 74,115

TABLE III

THE RESULTS OF MALE

Factor Age 0-6 Self-study Illiterate Primary school Junior high school

Weighting 0.266 318.518 63.0585 4.8712 5.3129

Rank 2

Factor Senior high school Junior college University Graduate school Unknown

Weighting 5.8537 39.3416 74.3899 435.743 35.3755

Rank 3 1

TABLE IV

THE RESULTS OF FEMALE

Factor Age 0-6 Self-study Illiterate Primary school Junior high school

Weighting 33.8425 692.568 47.7048 8.7881 1.3647

Rank 1 3

Factor Senior high school Junior college University Graduate school Unknown

Weighting 2.6591 2.5376 21.5129 128.602 3.3886

Rank 2

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