Design and Development of Decision Making System Using Fuzzy Analytic Hierarchy Process

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1 American Journal of Alied Sciences 5 (7): , 2008 ISSN Science Publications Design and Develoment of Decision Making System Using Fuzzy Analytic Hierarchy Process Chin Wen Cheong, Lee Hua Jie, Mak Chee Meng and Amy Lim Hui Lan Faculty of Information Technology, Multimedia University, Cyberjaya, Selangor, Malaysia Abstract: This article aims to develo a fuzzy Multicriteria Decision Making (MCDM) tool that equis with Analytic Hierarchy Process (AHP) framework to hel users in semistructured and unstructured decision making tasks. The tool rovides ortability and adatability features by deloying the software on web latform. In addition, this system rovides an integrated domain reference channel via a database connection to assist the user obtains relevant information regarding the roblem domain before constructing the AHP hierarchy attributes. Our decision making tool combines the characteristics of real time information retrieval through Internet and MCDM roblem analytical rocessing logic. Key words: Multicriteria decision making, analytic hierarchy rocess (AHP), fuzzy set theory INTRODUCTION Decision making analysis aims to realize conflicts that occur due to various different oinions, fluctuating environment conditions, subjective assessments, etc. In real world, decision often been made under various alternatives with their associated criteria. Imroer final selection may cause unleasant outcome with undesired results of misuse in resources, manower as well as recious time. Hence, it is imortant to achieve an otimal decision in real world roblems which involve multile alternatives and criteria in qualitative and quantitative domains. One of the famous Multicriteria Decision Making (MCDM) methodology is the Analytical Hierarchy Process (AHP) ioneers by Saaty [1,2]. Voluminous literatures have alied the framework of AHP for modeling unstructured roblems in the areas of economics [3,4], social [5], industrial [6,7] and military [8,9]. Due to its effectiveness and oularity, commercial software such as Exert Choice (htt://www. exertchoice.com), WebHIPRE (htt:// hut.fi), Criterium DecisionPlus (htt://www. infoharvest.com) and ERGO (htt://www. technologyevaluation.com) are adoting their systems and designs base on the AHP framework. One of the imortant rocedures in AHP is the airbyair comarison values for a set of redefined objects (alternatives). The AHP requires the decision makers furnish with comlete information and amle knowledge of all asects of the roblem statements during their judgments under a redefined semantic scale. However, the nature of the realworld roblems often relates to fuzziness and ambiguousness which initiates by the unrecedented environment conditions, human factors, incomlete information and etc. Numerous studies [1012] imlement the fuzzy set theory in the AHP roblem to tolerate the vagueness conditions. In this study, we develo an AHP multicriteria decision making tool which equis with fuzzy set theory [13] to tolerate the fuzziness in decision maker s judgements. Most of the current AHP decision suort commercial software is largely bases on the local machine executable format where user needs to setu the software rior to use. In our system design, we rovide ortability and adatability features by deloying the software on web latform. In addition, this tool rovides an integrated domain reference channel via a database connection to assist the end user obtain relevant information regarding the roblem domain before constructing the AHP hierarchy tree. Hence, our decision making tool combines the characteristic of real time information retrieval through internet and MCDM roblem analytical rocessing logic. MATERIALS AND METHODS System develoment: We select Visual Studio.NET (htt://msdn2.microsoft.com) as our comiler in the Corresonding Author: Chin Wen Cheong, Faculty of Information Technology, Multimedia University, Cyberjaya, Selangor, Malaysia 783

2 Am. J. Alied Sci., 5 (7): , 2008 software develoment hase. NET latform offers a new software develoment model that allows alications create in disarate rogramming languages to communicate with each other. In addition, NET architecture also offers Web services which allow alications in the Internet. C#.NET is our main language in the coding hase. We adot C#.NET alication into web alication using ASP.NET (htt:// We find it useful with various functions of ASP.NET to be deloyed into our tool. Among the alications of ASP.NET are session variables concets for assing data in different ages, usage of data grid and anels which are useful for structuring the outut, WYSIWYG (what you see is what you get) features and also suort various other third arty comonent. The system architecture design, state transition diagram and use case diagram are illustrated as follows: Diagram 1: State transition diagram Diagram 2: Architecture Design 784

3 Diagram 3: Use case Diagram Comutational algorithms Ste1: Fuzzy airwise comarison matrices: Due to simlicity and effectiveness, we select triangular fuzzy number as a reference to indicate the influence strength of each element in the hierarchy structure. Given a evaluation scale (Table 1) indicates from scores 1/9 to 9, the scores are fuzzified by the triangular fuzzy number f (l,m,u) where l and u are the lower and uer bounds that reresent the vagueness in the references scores. The fuzzy airwise comarison matrix, P %, is defines as: (1 1l1 1m 1 1u) (1 2l1 2m 1 2u) L (1 1n 1 nm 1 nu) (21 l21m 21u) (2 l22m 22u) L (2 nl2nm 2nu) (m1lm1m m1u) (m 2lm2m m2u) L (m nlmnm mnu) Ste 2 Fuzzy weighted erformance matrix: We define the weight measurement of each criterion and the erformance of resected alternative erformance as follows: ω % [(w w w ) (w w w )... (w w w )] j 1l 1m 1u 2l 2m 2u nl nm nu (a11la11ma 11u ) (a 21la 21ma 21u ). A % i ;.. (aijlaijma iju ) Am. J. Alied Sci., 5 (7): , Table 1: Evaluation scales Score fuzzy No. Score fuzzy No. 1 (1,1,1) if diagonal; 1/1 (1,1,1) if diagonal; (1,1,3) otherwise (1,1,3) otherwise 2 (1,2,4) 1/2 (1/4,1/2,1/1) 3 (1,3,5) 1/3 (1/5,1/3,1/1) 4 (2,4,6) 1/4 (1/6,1/4,1/2) 5 (3,5,7) 1/5 (1/7,1/5,1/3) 6 (4,6,8) 1/6 (1/8,1/6,1/4) 7 (5,7,9) 1/7 (1/9,1/7,1/5) 8 (6,8,10) 1/8 (1/10,1/8,1/6) 9 (7,9,11) 1/9 (1/11,1/9,1/7) where i 1,2,3 r, j 1,2,3 s and k r, or k s. After that, a fuzzy weighted erformance matrix (W) % can thus be obtained by multilying the weight vector with the decision matrix. (w1 la11lw1ma11mw1ua 11u ) (w2la21lw2ma21mw2ua 21u ). W% A % * % ; i ω j.. (wnmaij wnmaijmwnma iju ) l WW W WW W... WW W 1l 1m 1u 2l 2m 2u il im iu Ste 3: Fuzzy number ranking evaluation: In order to make a cris choice among the alternatives, we need to check and comare the ranking of the fuzzy numbers. We aly the alhacutsbased method 1 [14] to the total weighted erformance matrices for each alternative and check the ranking consistency for each alternative under different alha level. The alhacutsbased method 1 states that if let A % and B % be fuzzy numbers with cuts, A [a, a + ] and B [b, b + ]. It say A is smaller than B, denotes by A % B %, if a < b and a + < b + for all (0.1]. The advantage of this method is the conclusion is less controversial. Ste 4: Confidence level fuzzy number: A level threshold (0,,1) of the fuzzy set is defines to show the decisionmakers confidence to their judgements. The confidence value ranges between 0 and 1, from the least confidence to the most confidence. The definition of the symmetrical triangle fuzzy number (f (l,m,u)) with the interval confidence at level,, can be determined by:

4 Am. J. Alied Sci., 5 (7): , 2008 [ ] W Left (i) (ml)+l and resectively. [W 1left 1lright ] [W 2left 2right ]. W %, where.. [W ileft iright ] [ ( m u u] W Right ( i) ) + Ste 5: Otimistic level evaluations: The nature otimistic level of the decision maker can be otimistic, moderate or essimistic. The decision maker s otimistic level with fixed is denotes as: DM (i)w right (i)+(1)w left (i) Fig. 1: Main age where [0,1]. This cris erformance matrix is reresents by: C DM DM... DM (1) (2) ( i) Finally, we normalize the C(i)to evaluate the highest degree of suitability among the selection with resect to ialternatives using the following formula: C(i) C(i) C (i) EMPIRICAL APPLICATION Problem formulation: Consider a fresh graduate student would like to choose a job that can rovide overall satisfactions in term of benefits, colleagues, location and reutation. Says, the available jobs are job A, B and C. The roblem formulation rocess involves the goal, criteria and alternatives (three level hierarchy) as indicates in Fig. 1. When the user has a clear icture in mind regarding the roblem, one can start by inserting the values for each level in the main age. Else, the system rovides a domain information reository (DIR) and Google search to assist the user in roblem determination. 786 Fig. 2: Domain information reository (DIR) and Google search Pairwise comarison: After the roblem formulation (goal, criteria and alternatives), the system moves to the state of acceting airwise judgment from the user. The scoring scale is according to the Saaty s original scale [1,2]. Consistency checking: Before viewing the result of the AHP oeration, user can select PCM Consistency Check (Fig. 3) button to check whether the evaluations are consistent (Fig. 4) enough to be useful. If the evaluation is inconsistent, the system will alert the user to redefine the airwise comarison for the PCM.

5 Am. J. Alied Sci., 5 (7): , 2008 the information (criteria and alternatives) for certain common roblem domains. REFERENCES Fig. 5: Fuzzy Ranking Check Fig. 6: Synthesis Result for Fuzzy AHP In order to make a cris choice among the alternatives, alhacutsbased method is uses to check and comare the fuzzy number at all alha level at certain oint of otimistic threshold. Result visualization: Finally, the results are indicated in Fig. 6. CONCLUSION This rogram achieves simlicity and abstraction with fuzzy AHP algorithm that works behind the scene. The Web bases feature enhances the accessibility and ortability of this tool. In addition, we also integrate the domain information reository to assist the user with 1. Saaty, T.L., The Analytic Hierarchy Process. New York, McGraw Hill. 2. Saaty, T.L., Fundamentals of Decision making and riority theory with the Analytic Hierarchy Process. RWS Publications: Pittsburgh. 3. Ghodsyour, S.H. and C. O Brien, A decision suort system for sulier selection using an integrated analytic hierarchy rocess and linear rogramming. Int. J. Prod. Econ., 56: Badri, M.A., Combining the AHP and goal rogramming for global facility locationallocation roblem. Int. J. Prod. Econ., 62: Tsoi, R.H.L., Using analytic hierarchy rocess method to rioritise human resources in substitution roblem. Int. J. Comut. Internet Manage., 9: Chin, K.S., S. Chiu and V.M.R. Tummala, An evaluation of success factors using the AHP to imlement ISO based ESM. Int. J. Qual. Reliability Manage., 16: Udo, G.G., Using analytic hierarchy rocess to analyze the information technology outsourcing decision. Ind. Manage. Data Syst., 100: Cheng, C.H., Evaluating naval tactical missile systems by fuzzy AHP based on the grade value of membershi function. Eur. J. Oerat. Res., 96: Mon, D.L., Evaluating Weaon System Using Fuzzy Analytic Hierarchy Process Based on Entroy Weight. Proceedings of IEEE International Fuzzy Systems and The Second International Fuzzy Engineering Symosium, 2: Kahraman, C., U. Cebeci and D. Ruan, Multiattribute comarison of catering service comanies using fuzzy AHP: The case of Turkey. Int. J. Prod. Econ., 87: Kuo, R.J., C.C. Chi and S.S. Kao, A decision suort system for selecting convenience store location through integration of fuzzy AHP and artificial neural network. Comuters Industry, 47: Tam, M.C.Y. and V.M.R. Tummala, An alication of the AHP in vendor selection of a telecommunication system. Omega, 29: Chin, W.C., K.W.H. Yeow and K.L. Ng, Web server future lanning decision analysisfuzzy linguistic weighted aroach. Fourth International Conferennce on KnowledgeBased Intelligent Engineering Systems and Allied Technologies, Brighton UK., : Wang, L.X., Course in Fuzzy Systems and Control, Prentice Hall Inc. 787