MADM Methods in Solving Group Decision Support System on Gene Mutations Detection Simulation

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1 MADM Methods in Solving Group Decision Support Syste on Gene Mutations Detection Siulation Eratita *1, Sri Hartati *2, Retantyo Wardoyo *2, Agus Harjoko *2 *1 Departent of Inforation Syste, Coputer Science Faculty of Sriwaya University Indonesia (Doctoral Progra Student Coputer Science Gadjah Mada University ) Jl. Palebang-Prabuulih, Ogan Ilir, INDONESIA 1 eratitaz@yahoo.co * Departeent of Coputer Science and Electronics Matheatics and Natural Sciences Faculty Gadjah Mada University, Indonesia Abstract Detection of gene utation is an activity that can provide contribution in the edical field. Detection of utated gene is needed to avoid the diseases caused by the such as cancer. The detection of gene utations can be perfored by utilizing coputer-based syste. Group Decision Support Syste (GDSS) is a coputer-based syste that can be utilized in detecting huan gene utations that cause disease. The ELECTRE ethod, which is a Multi-Attribute Decision Making, is a ethod in odeling ulti-criteria GDSS. In this paper we propose a odel for ulti-criteria GDSS in which the siulation data is the utated genes that can cause cancer. Keywords: Group Decision Support Syste, ELECTRE, gene utation I. INTRODUCTION Gene Analysis has been carried out by various studies in the edical field, for exaple the detection of gene utated can cause huan threatening illness. Detection of utated gene causing cancer can be done through inforation technology. Deterining abnoral cancer caused by the genes can be ade fro various fields of edicine expertises, such as the field pathologist, onkology, etc. The opinions of the experts in various fields of edical science are required to construct a decision that could help to deliver edical action against a person alleged to have abnoral genes that cause cancer. The decision is defined as soe series of actions that need to be followed in solving the proble in order to avoid negative ipacts and exploit opportunities. The decision aking process should be used in solving the proble. Soeties the decision is constructed fro the decisions of soe groups. Decisions taken fro soe groups is called the group's decision, which can be assisted by using a support syste. This syste is known as group decision support syste. A Group Decision Support Syste (GDSS) is a coputer-based systes to support a collection of groups who have a coon task or goal. This syste typically provides an interface for users who are the eber of the group. The GDSS can accelerate decision-aking process or iprove the quality of the resulting decisions, or both. This can be done with the support for the exchange of ideas, opinions, and choices in the group on the syste. The Group Decision Support Syste can be applied to the field of inforation technology which is able to assist in providing decision regarding utated genes that ay or ay not cause cancer. Soe alternative ethods for the deterination of group decision aking have been iproved by researchers. This ethod was developed to deterine the best alternative fro several alternatives based on criterion in aking decisions. One of the ethod in decision aking group is Multiple Criteria Decision Making (MCDM). The MCDM is divided into two odels: Multi-Attribute Decision Making (MADM) and Multi-Objective Decision Making (MODM). The decision to justify whether the genes affected by genes causing cancer can be done by conducting ranking MCDM ELECTRE ethod. For that purpose, we need a odel in decisionaking process to detect the gene utations that can cause cancer. In this paper, we propose a GDSS Model by using the ELECTRE ethod to detect gene utations siulation. This odel is ade by using a siulation of the soe defined criteria. II. BACKGROUND THEORIES 2.1 GROUP DECISION SUPPORT SYSTEM (GDSS) GROUP DECISION SUPPORT SYSTEM (GDSS) is an interactive coputer based syste that facilitates solution of soe unstructured probles by a few (sets) of decision akers who work together as a group. GDSS can be applied to different groups of decision situations (group), which includes a review panel, task force executive eeting / board, reote workers, and so forth. The basic activities that occurred in any group and who require support on a coputer are: 1. Calling inforation, involving the selection of data values fro an existing database or calling siple inforation. 1

2 2. Inforation sharing, eaning the viewer displays the data on the screen to be viewed by groups. 3. Use of inforation, including application software technology, procedure, and group proble solving techniques to the data. [8] 2.2 MULTI- CRITERIA DECISION MAKING Multi-criteria decision aking (MCDM) is the decisionaking technique by considering soe alternatives options. The Decision aking MCDM technique is done by the selection or forulation of attributes, objectives, and different goals, in which these attributes, objective or purpose are considered as the criterion. The criteria are easures, rules or standards that guide the decision aking process. The criteria are built fro the basic huan needs and the values of interest. There are two kinds of categories of Multi-criteria decision aking (MCDM),[3], naely: 1. Multiple Objective Decision Making (MODM) 2. Multiple Attribute Decision Making (MADM) The Multiple Objective Decision Making (MODM) coes to the design, where atheatical optiization techniques are used. This types of MCDM is useful for a very large nuber of alternatives (up to infinity) and to answer the question about what and how uch. In addition, the MODM is used to solve probles in continuous space, such as probles in atheatical prograing. The MODM is design by using the best alternative. [3] The Multiple Attribute Decision Making (MADM), coes to elections, in which atheatical analysis is not needed. This type of MCDM can be used for the election in which there is only a sall nuber of alternative courses. The MADM is used to solve probles in discrete spaces, typically used to solve probles in the assessent and selection of liited nuber of alternatives. The MADM approaches are done through two stages, naely: 1. Perfor aggregation of the decisions that responds to the decisions corresponding to all destinations on each alternative 2. Perfor alternatives ranking based on the aggregation of the decision akers. [3] According[4]: MADM is evaluated against the alternative Ai (i = 1,2,..., ) against a set of attributes or criteria Cj ( j = 1,2,..., n) where each attribute are not utually dependent with each other. Decision atrix of each alternative on each attribute, is given as: x11 x12 x1n x x x x 21 1 x n xn Where x is an alternative perforance rating in relation to the j-th attribute. Weight value indicates the relative iportance of each attribute, given as, W: W = { w 1, w 2, w 3,, w n } Perforance rating () and weight value (W) represent the core values corresponding to the absolute preference of the decision akers. The MADM probles is finalized with an alternative process to get the best ranking obtained based on the overall value of granted preferences (Yeh, 2002) in [4].[4] 2.3 ELECTRE The ELECTRE (Eliination Et Choix Traduisant He realite) is based on the concept of ranking by paired coparisons between alternatives on the appropriate criteria. An alternative is said to doinate the other alternatives if one or ore criteria are et (copared with the criterion of other alternatives) and it is equal to the reaining criteria. Ranking relations are between two alternatives Ak fro the A1 (Roy, 1973) in [4]. Pairwise coparison of each alternative criteria in the sybolic (x ). Noralization of values was done by coparison (r ) into a scale using the forula: r i1 2, for i = 1,2,.., and j = 1,2,...,n (1.1) Factors of iportance (weight) is given to each criterion which is expressed in the relative iportance ( w j ) W = (w 1, w 2, w 3,...,w n ) N w j = 1; (1.2) i=1 This weight is then ultiplied by the atrix pairwise coparison atrix for V: V w x (1,3) j The foration of discorcodance - concordance index and the index for each pair of alternatives are done through assessent of the relation ranking. For each pair of alternatives A k and A 1 (k,l= 1,2,... dan k l ), the decision atrix for criterion j, are divided into two parts. The set of concordance index {c } shows the su of weights of criteria for which A k alternative is better than the A 1 alternative. C = { j v kj >v } for j = 1,2,...,n (1.4) The set of discordance index { d } forula : d = { j v kj <v } for j = 1,2,...,n (1.5) Matrix of concordance (C) contains eleents that in calculating the concordance index, and is associated with attribute weights are: C (1.6) w j jc The atrix of discordance (D) contains eleents of the discordance index is calculated according to (Triantaphyllou, 2000) in [4]. This atrix associated with the values of attributes, naely: 2

3 d ax v ax kj v jd vkj v j v j (1.7) These atrices can be built with the help of a threshold (threshold), c c k 1 l 1 c ( 1) (1.8) A k alternative ay have a chance to doinance A 1,, If concordance index exceeds the threshold c; c > c (1.9) and eleents of the atrix F is deterined as the doinant concordance : 1, jika c c f 0, jika c c (2.0) The sae is true for doinant discorcodance atrix G with d threshold. D values obtained with the forula: d k 1 l 1 d ( 1) (2.1) and eleents of the doinant F discordance atrix is deterined as : 1, jika d d g (2.2) 0, jika d d An Aggregation of the doinant atrix (E) showing a partial preference order of alternatives, obtained with the forula: e = f x g (2.2) If e = 1 indicates that the alternative A k ore on select fro the alternative A 1. [4] The researches on the ELECTRE ethod has been widely applied, for exaple: [9] conducted a study: The ELECTRE ethod based on interval nubers and its application to the selection of leather anufacture alternatives. In this study, it is studied how to ake use of traditional ethods for certain circustances to solve the MADM with interval nubers. The paper proposes an enhanced ELECTRE ethod based on the nuber of intervals. This is perfored by considering the specificity of interval nubers, using the possibility degree for ranking alternatives, founded the discordance doinance atrix and aggregate doinance atrix, then eliinating inferior alternatives. This ethod can be used to MADM, where the values of attributes in the for of interval nubers, and solve the difficulties in ranking a nuber of intervals in the traditional ethod. The selection of leather-aking proble solving with this ethod, and illustrated its application in real life. [9] In this study, using the possibility degree of interval to propose an alternative ranking and the ELECTRE ethod based on interval nubers, and it gives step to perfor using this ethod. This ethod can be used to solve the proble of ultiple solutions attribute decision in which the attribute values are nubers intervals. [9] [2] in his research on MADM ethods associated with the decision aker's point of view about the Iportance degree of responses. The results given is assued that the response-eans clustering is ore iportant than the standard deviation. Another advantage of this ethod is it considers the standard deviations that contribute to the strength of experiental design, because it only uses one appropriate response regression function, so that this ethod reduces the statistical error. Because this ethod attepts to obtain a value of several responses, then it can be grouped in the desirability function approach. [5] in his research develop ethods that VIKOR copared with ELECTRE II ethod in the ethod of ranking. Opricovic get the result that the siilarity of ELECTRE and VIKOR developent based on the equality principle as: (A) Consider the global certainty easure (concordance and group utility). (B) opsisi of other criteria-the-inority''''is not strong (nondiscordance). Analysis and ELECTRE VIKOR coparison shows that with the assuptions, conditions and decisions by Rj''discordance''in VIKOR have in coon with the basic MCDM (iniu individual regret). [7] in his research develop new ELECTRE Method with Interval Data in Multiple Attribute Decision Making Proble This study ai is to provide new and unique ethod for ranking alternatives with interval data in ulti-attribute decision aking. The use of interval data is considered better than to use the interval data for the deterinistic proble and the exact data (eg, tie, distance, teperature) or they can not easily be expressed as deterinistic and specific nubers. in this study, they developed a ethod for decision aking solution of probles (especially, when it is not possible to present the data so that the use of fuzzy fuzzy decision aking. [1] [7] conducted an applied research Analysis by an outranking ulti-attribute decision-aking technique, called Eliination et choix traduisant He realite ethod. This approach is applied to an illustrative exaple where Analytical hierarchy process ethod applied to calculate the global weights of the attributes of the couple through the coparison atrix. This study shows the proposed AHP- ELECTRE algorith; outranking relations between the alternatives and in this way, non-doinated sets of land-use alternatives other alternatives can be identified. In this approach, the worst alternative for the exaples given can be recognized as well. Results obtained by ELECTRE outranking is better than the TOPSIS ranking. This approach is beneficial especially when the nuber of alternatives ore. This eans that, further research is still needed to facilitate decision 3

4 aking MADM tool ore appropriate to apply in the field of MLSA. 2.4 ELECTRE METHOD FOR GENE MUTATIONS DETECTION SIMULATION This paper proposes a odeling of MADM with ELECTRE ethod to detect gene utations siulation in huans who suffer cancer. The utations that ight occur is that there is activation of the Rb gene c-yc gene or inactivation of p53 gene. In order to detect whether a person is identified to have cancer cells or not. The data were collected fro the study of gene utations [6] Table.1 Expression of protein p53,rb and c-yc 5 = Very good Level of iportance of each criterion in value by one to five, naely: 1 = very low 2 = Low 3 = enough 4 = High 5 = very high Fro the above criteria, a atch rating is ade for each alternative on each criterion. The rating a atch is ade by siulation, that in deterining the gene is utated or not that actually fit all the criteria and rating is obtained fro the opinions of experts. The siulated suitability rating of each criteria is indicated by the following table: Table.2 Suitability of each alternative on each criterion Alternatif Kriteria C1 C2 C3 A A A The calculation is done with the copletion ethod Eliination Et Choix Traduisant He realite (ELECTRE), which is based on the concept of ranking by paired coparisons between alternatives on the appropriate criteria. An alternative is said to doinate the other alternatives if one or ore criteria are et (copared to the criteria of other alternatives) and it is equal to the reaining criteria. The ranking relationship between the two alternatives A k and A 1 are denoted as A k A 1 if alternative-k no-one doinates the alternative to the quantitative, thus better decision akers to take risks A k than A 1 (roy, 1973) in [4]. Decision atrix of the siulation above obtained as follows: In this siulation, it can be applied to the three alternatives in the set to the identification of cancer cells in the huan gene, naely: A1 = Inactivasi p53 A2 = activation Rb A3 = c-yc activation Based on the gene expression in reference [6], there are three which reference in aking decisions to detect a person experiencing the gene utated, naely: C1 = p53 protein expression (in%) C2 = Rb expression (in%) C3 = c-yc expression (in%) The suitability rating alternatives on each criterion will be the value of the nubers one to five, naely: 1 = very bad 2 = bad 3 = enough 4 = Good Pairwise coparison of each alternative in each criteria is expressed by values (). This value ust be noralized to a scale coparable to (r ). This value is calculated with the forula as below: r i 1 2 dengan i = 1,2,..., j = 1,2...n (1.1) x 1 = x 3 = Fro the results of calculations using the above forula is obtained as the atrix below: 0, , , , , , , , ,

5 Furtherore, the V atrix is calculated based on the equation: V = w j x x Fro the above calculation results obtained by atrix V: 2, , , , , , , , ,46183 Calculated for the Association of concordance index (C ) that shows the su of weights of criteria, according to the forula; C = { j v kj >v } for j = 1,2,...,n (1.5) The results obtained with this calculation is as follows: C 12 : v 11 >v 21 2, > 2, V 12 >v 22 1, > 2,12132 V 13 >v 23 2,46183 > 1,96950 C 12 = {1,3} The sae calculation for each C then obtained value of C as follows: C 12 = {1,3} C 13 = {1,2,3} C 21 = {1,2} C 23 = {1,2} C 31 = {1,3} C 32 = {1, 3} Calculating the value set for the atrix discordonce discordonce associated with the attribute is the following: d = { j v kj <v } untuk j = 1,2,...,n (1.6) d 12 = v 11 <v 21 2, < 2, V 12 <v 22 1, < 2,12132 V 13 <v 23 2,46183 < 1,96950 d 12 = {2 } With a siilar calculation for each eleent of the set obtained value D: d 12 = { 2} d 13 = {} d 21 = {3} d 23 = {3} d 31 = {2} d 32 = {2} c concordance atrix eleents calculated using the forula : C (1.7) w j jc For w = 5,3,4 C 12 = {1,3}= w 1 + w 3 = 5 +4 = 9 C 13 = {1,2,3}= w 1 + w 2 + w 3 = = 12 C 21 = {1,2} = w 1 + w 2 = 5+3=8 C 23 = {1, 2} = w 1 + w 2 = 5+3=8 C 31 = {1,3} = w 1 + w 3 = 5 +4 = 9 C 32 = {1, 3}= w 1 + w 3 = 5 +4 = 9 Concordance atrix : C= d discordance atrix eleents calculated using the forula: axv kj vj d d ax v v kj j v j Matriks discordance: - 0,8 1 D= 0, ,8 - c k 1 l 1 c ( 1) c = = = 9,16 3(3-1) 6 d is calculated using the forula: d k 1 l1 d ( 1) 0, , ,8 4.8 d = = 6 6 d = 0,8 Concordance atrix calculated based on the doinant 1, jika c c f 0, jika c c F = (1.9) (2.0) eleents of the atrix F is deterined as the doinant discordance: 1, jika d d g 0, jika d d 5

6 - 1 1 G = Aggregation of the doinant atrix (E) showing a partial preference order of alternatives, obtained with the forula: e f. g 2.2) e = F x G = = Fro the above calculations A 2 doinate A 1, A 2 also doinate A 3. In this siulation, which deterined the criteria in Group Decision Support Syste in siulated fro existing data. To siulate the odel with the ELECTRE ethod is A 2 doinated A 1 and A 2 doinate A 3. This eans that in this siulation of the criteria for deterining the siulation showed that the activation of Rb ore likely to cause cancer. REFERENCES [1] Airi, Developing a New ELECTRE Method with Interval Data in Multiple Attribute Decision Making Probles 2008 [2] Bashiri, An Extension of Multi-Response Optiization In MADM view, Journal of applied Sciences 9(9); page , 2009 [3] R. Fitriadi, Pendekatan Coproise Prograing dengan eperhitungkan Faktor lingkungan (Studi Kasus Industri Otootif PT Jawa Tengah), Jurnal Iliah Teknik Industri Vol. 5 No. 2 Des 2006, hal 72 81, 2006 [4] S. Kusuadewi, S. Hartati, A. Harjoko, dan R. Wardoyo, Fuzzy Multi-Attribute Decision Making (FUZZY MADM), Yogyakarta: Penerbit Graha Ilu, 2006 [5] S. Opricovic, G.H. Tzeng, Extended VIKOR ethod in coparison with outranking ethods, European Journal of Operational Research 178 (2007) , 2007 [6] A. Prayitno, et All, The expression of p53, Rb, and c-yc protein in cervical cancer by iunohistocheistry stain, Biodiversitas ISSN: Volue 6, Noor 3 Juli 2005 Halaan: , 2005 [7] Soltanohaadi, Achieving to soe outranking relationships between post ining land uses through ined land suitability analysis, Int. J. Environ. Sci. Tech., 5 (4), , Autun 2008 ISSN: Irsen, Ceers, IAU, 2008 [8] E. Turban, Dicision Support and Expert Systes: Manageent Support Systes, Fourth Edition, Prentice-Hall,Inc., United State, 2005 [9] Q. Zhang and J. Ma, Deterining Weights of Criteria Based on Multiple Preference Forats, online pada /WorkingPapers/paper/0102.pdf 12 Oktober 2004, 2004 III. CONCLUDING REMARKS AND FURTHER WORKS Group Decision-aking can assist in decisions ade by a group of people. There are soe group decision aking ethods have been developed, and ELECTRE ethod is one of the ethod in group decision aking that can assist in the decision aking process to deterine whether a utated gene can cause cancer or not, based on existing criteria in the gene utation. This paper proposes the criteria in a for siulation odeling using ELECTRE ethod. The results fro the decisions is based on the deterination of criteria for odeling. The deterination of criteria for deterining whether a utated gene can cause cancer or do not has to refer to experts in their fields. This paper deonstrates the odeling to perfor the calculation so that the decision can be odelled by using these calculations. This ade the odelling flexible in accordance with the criteria established by the experts for decision aking, so that the utated gene for the deterination of a person or not the criteria derived fro expert opinion in the edical field. This odeling can be used for real life criteria, based on criteria established by the experts. 6