Fuzzy Topsis Method

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Fuzzy TOPSIS method
This is an approach based on the TOPSIS technique (Technique for Order Preference by Similarity to Ideal Solution) and the fuzzy set theory. The TOPSIS method is based on the concept that the optimum option has the least distance from the positive ideal solution. It is a linear weighting technique, which was first proposed, in its crisp version by Chen and Hwang(1992), with reference to Hwang and Yoon(1981). Since then, this method has been widely adopted to solve MCDM problems in many different fields. Because decision information is uncertain instead of certain in most environments, further extension for group decision making problems under fuzzy environment was published by Cheng(2000),known as Fuzzy TOPSIS. The selection of the third-party provider is a typical MCDM problem. In this method firstly we screen out providers that have not minimal qualifications by the selection criteria. Then closeness coefficient of contractors to each proposal will be computed by Fuzzy TOPSIS method and finally these coefficients as successful indicators for each provider will be fed in to a linear programming to select most profitable projects and providers with respect to the constraints. The stages are described blow: Stage1: Eliminate contractors that haven't minimal qualifications. For the purpose of analysis, selection criteria need to be rationally selected at first. There are a lot of researches with respect to the decision criteria for evaluating the supplier. Such as the study of Dickson(1966), Ellram (1990),Weber et al.(1991), ,Grupe (1997), and Akomode et al.(1998). According to an empirical survey, the top four selection criteria are responsiveness to service requirements, quality of management, track record of ethical importance, and ability to provide value-added services. The less important selection criteria are listed in a descending order as below: low cost, specific channel expertise, knowledge of market, personal relationship with key contacts, willingness to assume risk, investment in state-of- art technologies, size of firm, and national market coverage. Keeping the outcomes of the supplier selection literature review as a guideline, we derived the relevant factors to evaluate in the provider selection process based on the outsourcing view. However selection of criteria is totally industry specific and based on each case and the criteria are changed and replaced. Then opinions of decision makers on criteria were aggregated and weights of all criteria have been calculated by organizing the expert meeting. Meanwhile, the outcomes of the supplier selection literature review should be kept as a guideline.

Stage2: Computing closeness coefficient (CC) for each project by fuzzy TOPSIS method So after we have obtained the important evaluation criteria and the qualified provider candidates to form the MCDM problem,the ranking of the shortlisted vendor providers will be done using the fuzzy TOPSIS approach. First,choose the appropriate linguistic variables for the importance weight of the criteria ,asses the importance of each contractor in each project with respect to each criterion by DM, using linguistic variables. Convert these evaluation into triangular fuzzy numbers with fuzzy weight for each criterion. Fuzzy weight wj of criterion C j are obtained with regard to DM’s opinions. Then the importance of the criteria and the rating of alternatives with respect to each criterion and the aggregated rating Xij under criteria C j can be calculated as: Wj=1K[Wj1+Wj2+…+Wjk]

xij=1K[xij1+xij2+…+xijk]
Wjk is the importance weight of the kth decision maker.
xijk is the rating of the kth decision maker.
Construct the normalized fuzzy decision matrix. If we describe the linguistic variables by triangular fuzzy numbers, xij=(aij,bij,cij) and wij=(wj1,wj2,wj3)then we can get the fuzzy decision matrix denoted by R, and R= R=[rij]m×n. rij=(aijcj,bijcj,cijcj)

rij=(aj-aij,aj-bij,aj-cij)
Next, the weighted...
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