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Apply Grey Relational Grade And Rough Set Theory for The Factor

Weighting Analysis in Liver Function

1 Kun-Li Wen, 2Mei-Li You,

3Bih-Yun Lee

*1,Corresponding Author Department of Electrical Engineering, Chienkuo Technology University (GSRC),

Changhua, Taiwan, [email protected] 2Department of General Education, Chienkuo Technology University, Changhua, Taiwan

[email protected] 3 Department of Health Executive Yuan Central Laboratory Central Region Hospital Alliance,

Taichung, Taiwan, [email protected]

Abstract This paper is mainly a continuation of the previous paper, which is based on an assessment of liver

function and verifies the results. First of all, we use the grey relational grade in grey system theory and

integrate the numerical results of the examiner. And then, the influence factors of liver function toward

weighting value are derived by significant in rough set theory. In addition, by using software, toolbox

concept and the powerful function of software application, that is based on a relevant measuring model

and weighting model to develop a toolbox and to achieve a practical setting and academic research.

The paper mainly does an in-depth analysis on liver function diagnosis. In order to achieve the

purpose, we first refer to the relevant regulation of Department of Health and decide the analyzed

influence factors of diagnosis. In addition, we suggest five influence factors according to the past

researches and the current medical analysis factors. In order to explore the nature of each factor, the

expected input data is over 300 cases. Secondly, we make use of grey relational grade in grey system

theory to convert a subjective judgment into an objective way of quantitative value, and take the value

as the output of weighting analysis. Then, the influence factors of liver function toward system’s

objective weighting are derived by means of significant model in rough set theory. During the setting

period, we also develop a Matlab toolbox and support with lots of calculation and complicate

mathematical calculation due to the mutual influence of objects data. In addition to complete a medical

assistance platform of the objective intelligent liver function evaluation, we continuously pile up the

evaluation software of medical system.

Keywords: Liver Function, Grey Relational Grade, Significant, Rough set Theory, Toolbox,

Influence Factor

1. Introduction

According to the recent reports of the Department of Health, liver disease has become the first place

of domestic Taiwan diseases. Over 7,000 people died of liver cancer and about 5,000 people died of

cirrhosis. Adding up with hepatitis and people who died of liver disease, In general, there are a lot of

people suffer from hepatitis, and there are still over eleven thousand people die of liver disease

annually. The death rate of liver disease has exceeded yearly average[1,2].

At present, liver function evaluation is normally used in the ordinary hospitals. The test items are

often quite simple which only focuses on two items: AST and ALT. Other relevant factors are optional

unless they are necessary to the patients. Making a further decision-making, the Medicare development

is still inadequate.

Besides, in the past research, there were many liver disease researches in this field. Most of them are

analysis about liver function index which means AST, ALT and GTP index of blood. It is only used to

diagnose HIV infection, chronic hepatitis, fatty liver, liver cell necrosis and ischemic liver damage. It

doesn’t pay attention to the analysis of liver function impact factors. In addition, there’s no related

biological and chemical testing standard and importance on the relevant testing items[3~8].

Therefore, this study is mainly a continuation of the previous verification result and evaluation of

liver function evaluation. First of all, we use the grey relational grade in grey system theory to integrate

the numerical results of the examiner, and get the quantitative numerical results of biochemical testing.

Apply Grey Relational Grade And Rough Set Theory for The Factor Weighting Analysis in Liver Function Kun-Li Wen, Mei-Li You, Bih-Yun Lee

Journal of Convergence Information Technology(JCIT) Volume6, Number9, September 2011 doi:10.4156/jcit.vol6.issue9.49

420

And then, the impact factors of liver function toward weighting value are derived by significant in

rough set theory[9~12]. In addition, by using computer software, computer toolbox and the powerful function of software

application that is based on a relevant measuring model and weighting model to develop a computer

toolbox and to achieve a practical setting and academic research[13,14].

In this paper, first, in section 2, the mathematics concept of grey relational grade and the basic

concept of rough set theory are presented respectively. Section 3 is the real example in liver function

evaluation; also the development of toolbox is introduced. Also in section 4, we make some advantages

and suggestions for the further research in our study.

2. Mathematics Model

2.1 The grey relational grade

The grey relational grade is the most important in the relational analysis, and the main function is

the measurement between two discrete sequences[15]. The mathematical foundation of grey relational

grade can be described as follows.

1. Factor space

Assume )(XP is one theme and Q is one relationship. If a characteristic exists with key factors, such

as: countable intention factor, expansion of factor and independence factor for the combination of

{ )(XP ; Q }, then it can be called a factor space.

2. The comparison of sequence

Assume a sequence as

))(,,)(),(()( 21 kxkxkxkx ni (1)

where: nink ,3,2,1 ,,3,2,1 , and meet the following three conditions: Non-dimensional,

Scaling and Polarization, thus, this sequence is comparable.

3. The four axioms of grey relational measurement

The space is called grey relational space and is demonstrated by { )(XP ;}, in which { )(XP } is

the theme and is the measurement tool, and have four axioms: Normality, Duality Symmetric,

Wholeness and Closeness.

According to the above descriptions, if a function ),( ji xx can be found to meet all of the

above four axioms, ),( ji xx is considered as a grey relational grade. Now, we assume the sequences:

Xkxxxx iiii � ))(,,,)2(,)1(( , where mi ,,2,1,0 , Nnk � ,,3,2,1 .

If the 0x is the reference sequence, and the others are inspected sequences, then, it is called the

localization grey relational grade.

))(,,,)2(,)1((

))(,,,)2(,)1((

))(,,,)2(,)1((

))(,,,)2(,)1((

2222

1111

0000

kxxxx

kxxxx

kxxxx

kxxxx

mmmm

(2)

According to the past reference, meantime, there have six kinds of grey relational grades [6]. In our

paper, we use Nagai’s cardinal type method as our mathematics model.

.min.max

0.max00 ) ,(

i

ii xx , 2

1

1

2

00 )(1

n

k

ii kn

(3)


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where: i. Ijnkmi � ,,,3,2,1 ,,,3,2,1

ii. 0x is reference sequence, ix are inspected sequences.

iii. | |)()(| |)( 0 kxkxk ioi the norm between 0x and ix .

iv. ||)()(|| 0

.min.min

.min kxkxk jij

, ||)()(|| 0

.max.max

.max kxkxk jij

, i0 : The mean of i0

2.2 Rough set theory

In this section, we only simply introduce the basic concept of rough set[9].

1. Information system

),( AUIS is called information system, where },.....,,,{ 321 nxxxxU is the universe finite set of

object, and },...,,,{ 321 maaaaA is the set of attribute.

2. Information function

If exist a mapping aa VUf : , then aV is the set of value of a, call the domain of attribute a .

3. Discrete: The mathematics model of equal interval width is

k

VVt .min.max (4)

where: .maxV : Maximum value in the data. .minV : Minimum value in the data, means that the range

of attribute value is ],[ min.max VV .

According to the result, we can get the interval corresponding to attribute value are

]},[,],,[],,{[ 12110 kk dddddd (5)

where: kiddVdVd iik ,,3,2,1,,, 1maxmin0 , k is the grade of discrete.

4. Lower approximations and upper approximations

If UA , then the lower approximations and the upper approximations are defined as

}][| {x)( AxUAR R }][|]{[ AxR

Ux RR , }|{][ Ryxyx R (6)

}][| {x)( AxUAR R }][|]{[ AxR

Ux RR , }|{][ Ryxyx R (7)

In other words, the lower approximation of a set is the set of all elements that surely belongs to U,

whereas the upper approximation of U is the set of all elements that possibly belongs to U.

5. Indiscernibility: An indiscernibility relation is defined as for any ix and jx , if ix is identical to jx ,

then ix and jx have all the same properties.

6. Positive, negative and boundary: Base on the mentioned above, the positive, negative and boundary

are

)()( XRXposR , )()( XRUXnegR , )()()( ARARAbnR (8)

7. The dependents of attributes: The dependents of attributes is defined as

U

DposcDc (9)


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8. The significant value of attributes: In decision system, fVDCUS ,,, , under Ca , the

significant value of attributes is defined as

D

DDa

c

accDC

,

(10)

3. The Analysis of Influence Factors in Liver Function

3.1 The preprocessing of liver function

There are 12 liver function indicators in the current liver function analysis [16].

Table 1. The item of live function

No Factor No Factor

1 The Alanine Aminotransferase(AST)) 7 The Total Bilirubin(T-Bilirubin)

2 The Aspartate Aminotransferase(ALT) 8 The Direct Bilirubin(D-Bilirubin)

3 The Total Protein(T-Protein) 9 The Alkaline Phosphataes(ALK-P)

4 The Albumin(Albumin) 10 The gamma Globulin Total Protein( GTP )

5 The Globulin(Globulin) 11 The Creatine phosphor kinase(CPK)

6 The ratio of Albumin and Globulin(A/G) 12 The Lactic dehydrogenase(LDH)

Based on the past researchers, item 1, item 2, item 4, item 7 and item 12 are the most important

influencing factors.

Table 2. The item of live function

No. Item Range

1 Alanine Aminotransferase: AST [15, 41]

2 Aspartate Aminotransferas: ALT [10, 40]

4 Albumin [3.5, 4.8]

7 The Total Bilirubin: T-Bilirubin [0.2, 1.2]

12 The Lactic Dehydrogenase: LDH [100, 189]

According to the Department of Health, Executive Yuan’s data, the original mass collected data of

testing subjects were from various hospitals without any age and gender differences. Therefore, based

on Table 3, we divide the impact factors into four levels. Each level’s scope is shown in Table 3 and

Table 4.

Table 3. The grade and range for each factor Grade-I Grade-II Grade-III Grade-IV

AST* )5.21,15[ )28,5.21[ )5.34,28[ ]41,5.34[

ALT* )5.17,10[ )25,5.17[ )5.32,25[ ]40,5.32[

Albumin** )5.4,8.4[ )2.4,5.4[ )9.3,2.4[ ]5.3,9.3[

T-Bilirubin* )45.0,20.0[ )70.0,45.0[ )95.0,70.0[ ]20.1,95.0[

LDH* )25.122,100[ )5.144.,25.122[ )75.166,5.144[ ]189,75.166[

*smaller the better **Large the better

From Table 3, first of all, ix acts as the testing subject and the classification scope is indicated as

four standard sequences from Ix to IVx , as shown in Table 4.


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Table 4. Four standard sequences from Ix to

Grade-I: Ix =(15.00,10.00, 4.80, 0.20, 100)

Grade-II: IIx =(21.51,17.51, 4.51, 0.45, 122.25)

Grade-III IIIx = (28.01,25.01, 4.21, 0.70, 144.5)

Grade-IV: IVx =(34.51,32.50, 3.91, 0.95, 166.75)

3.2 Real case in liver function

The number of real case are 312, includes 216 male and 96 female, the whole data are shown in

Table 5 [17].

Table 5. The data of 312 subjects Factor & No. AST ALT Albumin T-Bilirubin LDH

001 30 33 4.8 0.4 135 002 19 22 4.6 0.5 153 003 29 19 4.5 0.8 137 004 23 25 4.5 0.7 164 005 25 28 4.5 0.9 175 006 17 16 4.4 1.0 129 007 24 18 4.4 0.9 163 008 20 11 4.3 0.8 154 009 15 12 4.3 0.6 136 009 15 12 4.3 0.6 136

307 30 29 3.7 0.7 126

308 30 32 4.1 0.7 189

309 25 33 4.0 0.8 143

310 26 34 4.6 0.6 176

311 27 38 4.0 0.4 145

312 29 39 4.0 1.2 139

Substitute measurement data into equation (3) to get the grey relational grade of subject, which the

standard sequences are Grade-I, Grade-II, Grade-III and Grade-V. After the grey relational grade in

each grade had found, substitute into equation (11) to get the health score, as shown in Table 7.

Health score=

4

14

1

i

i (11)

For example, in No. 001 subject, the sequence 1x =(30, 33, 4.8, 0.4, 135), and the standard

sequences are Ix =(15.00,10.00, 4.80, 0.20, 100), IIx =(21.51,17.51, 4.51, 0.45, 122.25), IIIx =

(28.01,25.01, 4.21, 0.70, 144.5) and IVx =(34.51,32.50, 3.91, 0.95, 166.75). Based on equation (3), the

grey relational grade are I1 =0.5267, II1 =0.8127, III1 =0.9091, and IV1 =0.8004. Substitute into

equation (11), then the health score for subject No. 001 is 0.7622. Same as the above analysis steps, the

health score from 002 to 312 can be found, and all are listed in Table 6.


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Table 6. The grey relational grade for 312 subjects No GRG No GRG

001 0.7622 301 0.7873 002 0.7289 302 0.7916 003 0.7874 303 0.7385 004 0.6745 304 0.7803 005 0.6009 305 0.7896 006 0.7957 306 0.7719 007 0.6767 307 0.7753 008 0.7072 308 0.4882 009 0.7677 309 0.756 010 0.6937 310 0.5858

311 0.7282

312 0.7323

3.3 The finding of weighting for each factor

Use equation (4) to discrete the subject data at first, as shown in Table 7, when the discrete data e of

each subject are found, by setting the decision factor is the grey relational grade(health score), and

attribute factors are AST, ALT, Albumin, T-Bilirubin and LDH.

Table 7. The discrete of subject data (five grades) Factor & No. AST ALT Albumin T-Bilirubin LDH GRG

001 4 5 5 2 4 5 002 2 3 5 2 5 5 003 4 3 5 4 4 5 004 3 4 5 3 5 5 005 3 4 5 4 5 4 006 2 2 5 5 4 5 007 3 3 5 4 5 5 008 2 2 5 4 5 5 009 2 2 5 2 4 5 009 4 2 5 5 3 5 010 4 5 5 2 4 5

301 3 3 3 2 4 5 302 3 4 3 3 4 5 303 3 4 4 4 5 5 304 3 4 4 5 4 5 305 3 4 4 3 4 5 306 4 4 4 5 4 5 307 4 4 4 3 4 5 308 4 5 4 3 5 3 309 3 5 4 4 4 5 310 3 5 5 2 5 4 311 3 5 4 2 4 5 312 4 5 4 5 4 5

Use equation (9) and equation (10) to get the weighting for each influence factor, the results are

shown in Table 8.

Table 8. The weighting for influence factor

Factor. AST ALT Albumin T-Bilirubin LDH

Significant 0.061 0.0576 0.0576 0.0678 0.2102

3.4 The characteristics of toolbox

Because of the amount of data is enormous; therefore, the computer toolbox is also developed to

analyze and verify our approach, and the results are list from Fig. 1 to Fig. 3[17].


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Figure 1. The results of grey relational grade (health score)

Figure 2. The results of discrete in rough set

1

2

3 4

5

1

2

3

4

5

6


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Figure 3. The results of significant in rough set

4. Conclusion

Most of the past weighting researches of liver function impact factors adopted traditional statistical

analysis so that a great deal of information is required. It is not only difficult to cope with clinical

researches, but also loss of authenticity. Besides, the testing factors are very simple and the other

relevant testing factors are relatively not necessary. As the results, we have an interesting result that the

most important influence factor is LDH, and the others four factors are in the same group. Through this

study, two contribute are presented, one is an objective weighing analysis of liver function evaluation

impact factors to the system in health care field, and the other is a Matlab GUI grey relational grade

and a significant in rough set computer toolbox are developed by the type of man-machine interface.

Based on the research processing, more number of data can make the mathematical analysis more

precise and more matching to the actual situation. Also more influence factor is also considered in the

further research.

To sum up, this study establishes a set of platform to support medical care evaluation. It not only

promotes the medical quality, but also acts as a reference for continuous researches in the field.

5. Acknowledgements

The authors want to heartily thank NSC, for this article was extension series form the project in

NSC 99-2221-E-270-008.

6. References

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Advances in Computer and Engineering, pp. 238-242, 2010.

[4]H. Y. Ying Chen, Applied grey relational analysis in the liver function and the development of

Matlab toolbox, Master thesis, Department of Automation Engineering & Institute of

Mechatronoptic Systems, Chienkuo Technology University, 2009.

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