Apply Grey Relational Grade And Rough Set Theory for The Factor Weighting Analysis in Liver Function

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1 Apply Grey Relational Grade And Rough Set Theory for The Factor Weighting Analysis in Liver Function Kun-Li Wen, Mei-Li You, 3 Bih-Yun Lee *,Corresponding Author Department of Electrical Engineering, Chienkuo Technology University (GSRC), Changhua, Taiwan, klw@ctu.edu.tw Department of General Education, Chienkuo Technology University, Changhua, Taiwan mei@ctu.edu.tw 3 Department of Health Eecutive Yuan Central Laboratory Central Region Hospital Alliance, Taichung, Taiwan, bihyun55@gmail.com 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 eaminer. And then, the influence factors of liver function toward weighting value are derived by significant in rough set theory. In addition, by using software, toolbo concept and the powerful function of software application, that is based on a relevant measuring model and weighting model to develop a toolbo 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 eplore the nature of each factor, the epected 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 toolbo 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, Toolbo, Influence Factor. Introduction Apply Grey Relational Grade And Rough Set Theory for The Factor Weighting Analysis in Liver Function 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 eceeded yearly average[,]. 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 inde which means AST, ALT and GTP inde 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 eaminer, and get the quantitative numerical results of biochemical testing. Journal of Convergence Information Technology(JCIT) Volume6, Number9, September 0 doi:0.456/jcit.vol6.issue

2 And then, the impact factors of liver function toward weighting value are derived by significant in rough set theory[9~]. In addition, by using computer software, computer toolbo and the powerful function of software application that is based on a relevant measuring model and weighting model to develop a computer toolbo and to achieve a practical setting and academic research[3,4]. In this paper, first, in section, the mathematics concept of grey relational grade and the basic concept of rough set theory are presented respectively. Section 3 is the real eample in liver function evaluation; also the development of toolbo is introduced. Also in section 4, we make some advantages and suggestions for the further research in our study.. Mathematics Model. 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[5]. The mathematical foundation of grey relational grade can be described as follows.. Factor space Assume P(X ) is one theme and Q is one relationship. If a characteristic eists with key factors, such as: countable intention factor, epansion of factor and independence factor for the combination of { P (X ) ; Q }, then it can be called a factor space.. The comparison of sequence Assume a sequence as i( n k k) ( ( k), ( k),, ( )) () where: k,,3,, n i,,3, n, and meet the following three conditions: Non-dimensional, Scaling and Polarization, thus, this sequence is comparable. 3. The four aioms of grey relational measurement The space is called grey relational space and is demonstrated by { P (X ) ;}, in which { P (X ) } is the theme and is the measurement tool, and have four aioms: Normality, Duality Symmetric, Wholeness and Closeness. According to the above descriptions, if a function i, ) can be found to meet all of the ( j above four aioms, i, ) is considered as a grey relational grade. Now, we assume the sequences: ( j ( (), (),,, ( k)) X, where i 0,,,, m, k,,3,, nn. i i i Apply Grey Relational Grade And Rough Set Theory for The Factor Weighting Analysis in Liver Function i If the 0 is the reference sequence, and the others are inspected sequences, then, it is called the localization grey relational grade. 0 ( (), (),,, ( k)) 0 ( ( 0 ( (), (),,, ( k)) m m (), (), 0 (),,, m (),,, ( k)) m ( k)) () According to the past reference, meantime, there have si kinds of grey relational grades [6]. In our paper, we use Nagai s cardinal type method as our mathematics model. n ma. 0i 0 i ( 0, i ), 0 i 0 ( ) ma. i k min. n k (3) 4

3 where: i. i,,3,, m, k,,3,, n, j I ii. 0 is reference sequence, i are inspected sequences. iii. oi( k) 0( k) i ( k) the norm between 0 and i. min.min. iv. k 0( k) ( k) min. ji. Rough set theory j ma.ma., ma. k 0( k) j ( k) ji, 0i : The mean of 0i In this section, we only simply introduce the basic concept of rough set[9].. Information system IS ( U, A) is called information system, where U,,,..., } is the universe finite set of { 3 n object, and A { a, a, a 3,..., a m} is the set of attribute.. Information function If eist a mapping fa : U Va, then V a is the set of value of a, call the domain of attribute a. 3. Discrete: The mathematics model of equal interval width is Vma. Vmin (4) k t. where: V ma. : Maimum value in the data. V min. : Minimum value in the data, means that the range of attribute value is [ V ma., V min ]. According to the result, we can get the interval corresponding to attribute value are {[ d0, d],[ d, d],,[ d k, dk ]} (5) where: d0 Vmin, dk Vma, di di, i,,3,, k, k is the grade of discrete. 4. Lower approimations and upper approimations If A U, then the lower approimations and the upper approimations are defined as R( A) { U [ ] R A} {[ ] U R R [ ] R A}, [ ] R { y Ry} (6) R( A) {U [ ] R A } {[ ] U R R [ ] R A }, [ ] R { y Ry} (7) In other words, the lower approimation of a set is the set of all elements that surely belongs to U, whereas the upper approimation of U is the set of all elements that possibly belongs to U. 5. Indiscernibility: An indiscernibility relation is defined as for any i and j, if i is identical to, then i and Apply Grey Relational Grade And Rough Set Theory for The Factor Weighting Analysis in Liver Function j have all the same properties. 6. Positive, negative and boundary: Base on the mentioned above, the positive, negative and boundary are pos R ( X ) R( X ), neg R ( X ) U R( X ), bn R ( A) R( A) R( A) (8) 7. The dependents of attributes: The dependents of attributes is defined as posc D cd (9) U j 4

4 8. The significant value of attributes: In decision system, S U, C D, V, f significant value of attributes is defined as, under a C, the c D c a D C Da (0), D c 3. The Analysis of Influence Factors in Liver Function 3. The preprocessing of liver function There are liver function indicators in the current liver function analysis [6]. Table. The item of live function No Factor No Factor The Alanine Aminotransferase(AST)) 7 The Total Bilirubin(T-Bilirubin) 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) 0 The gamma Globulin Total Protein( GTP ) 5 The Globulin(Globulin) The Creatine phosphor kinase(cpk) 6 The ratio of Albumin and Globulin(A/G) The Lactic dehydrogenase(ldh) Based on the past researchers, item, item, item 4, item 7 and item are the most important influencing factors. Table. The item of live function No. Item Range Alanine Aminotransferase: AST [5, 4] Aspartate Aminotransferas: ALT [0, 40] 4 Albumin [3.5, 4.8] 7 The Total Bilirubin: T-Bilirubin [0.,.] The Lactic Dehydrogenase: LDH [00, 89] According to the Department of Health, Eecutive 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,.5) [.5,8) [ 8,34.5) [ 34.5,4] ALT* [ 0,7.5) [ 7.5,5) [ 5,3.5) [ 3.5,40] Albumin** [ 4.8,4.5) [ 4.5,4.) [ 4.,3.9 ) [ 3.9,3.5 ] T-Bilirubin* [ 0.0,0.45) [ 0.45,0.70) [ 0.70,0.95) [ 0.95,.0] LDH* [ 00,.5) [.5.,44.5) [ 44.5,66.75) [ 66.75,89] *smaller the better **Large the better From Table 3, first of all, i acts as the testing subject and the classification scope is indicated as four standard sequences from I to IV, as shown in Table 4. 43

5 Grade-I: Grade-II: Grade-III Grade-IV: Table 4. Four standard sequences from to I =(5.00,0.00, 4.80, 0.0, 00) II =(.5,7.5, 4.5, 0.45,.5) III = (8.0,5.0, 4., 0.70, 44.5) IV =(34.5,3.50, 3.9, 0.95, 66.75) I 3. Real case in liver function The number of real case are 3, includes 6 male and 96 female, the whole data are shown in Table 5 [7]. Table 5. The data of 3 subjects Factor & No. AST ALT Albumin T-Bilirubin LDH 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 () to get the health score, as shown in Table 7. Health score= 4 4 i i () For eample, in No. 00 subject, the sequence =(30, 33, 4.8, 0.4, 35), and the standard sequences are I =(5.00,0.00, 4.80, 0.0, 00), II =(.5,7.5, 4.5, 0.45,.5), III = (8.0,5.0, 4., 0.70, 44.5) and IV =(34.5,3.50, 3.9, 0.95, 66.75). Based on equation (3), the grey relational grade are I =0.567, II =0.87, III =0.909, and IV = Substitute into equation (), then the health score for subject No. 00 is Same as the above analysis steps, the health score from 00 to 3 can be found, and all are listed in Table 6. 44

6 Table 6. The grey relational grade for 3 subjects No GRG No GRG 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 Use equation (9) and equation (0) 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 The characteristics of toolbo Because of the amount of data is enormous; therefore, the computer toolbo is also developed to analyze and verify our approach, and the results are list from Fig. to Fig. 3[7]. 45

7 Figure. The results of grey relational grade (health score) Figure. The results of discrete in rough set 46

8 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 toolbo 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 etension series form the project in NSC 99--E References [] The Department of Health, Eecutive Yuan, National health report, 0. []S. S. Hung, The compliance and determinants of clinical guidelines of liver disease in Taiwan, Master thesis, Institute of Hospital and Health Care Administration, National Yang-Ming University, 009. [3]K. L. Wen, B. Y. Lee, M. L. You and Z. S. Zhou, The development of Matlab toolbo for liver function evaluation, IASTED 6 th Advances in Computer and Engineering, pp. 38-4, 00. [4]H. Y. Ying Chen, Applied grey relational analysis in the liver function and the development of Matlab toolbo, Master thesis, Department of Automation Engineering & Institute of Mechatronoptic Systems, Chienkuo Technology University,

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