Fuzzy Topsis Method

Fuzzy TOPSIS manner This is an approach establish on the TOPSIS technique (Technique for Order Preference by Similarity to elevated Solution) and the clouded set theory. The TOPSIS method is based on the concept that the best option has the least distance from the prescribed ideal stem. It is a additive cant overing technique, which was first proposed, in its crisp version by subgenus Chen and Hwang(1992), with reference to Hwang and Yoon(1981).Since then, this method has been widely adopted to solve MCDM problems in umpteen different fields. Because conclusion information is uncertain instead of certain in intimately environments, further extension for group decision making problems low haired environment was published by Cheng(2000),known as Fuzzy TOPSIS. The excerpt of the third-p tricky contributer is a typical MCDM problem. In this method firstly we separate out providers that have not nominal qualifications by the woof criteria. consequently conversancy coeff icient of contractors to distributively 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 heed to the constraints. The stages argon described blow Stage1 Eliminate contractors that havent minimal qualifications. For the purpose of analysis, selection criteria pick out to be rationally selected at first. thither are a lot of researches with respect to the decision criteria for evaluating the supplier.Such as the hit the books 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 go order as below low cost, specif ic channel expertise, association 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 canvass 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 fabrication specific and based on each outcome and the criteria are changed and replaced. Then opinions of decision makers on criteria were add up and cant overs of all criteria have been metric by organizing the expert meeting. Meanwhile, the outcomes of the supplier selection literature review should be unplowed as a guideline.Stage2 Computing closeness coefficient (CC) for each project by fuzzy TOPSIS method So after we have obtained the important valuation criteria and the qualified provider candidates to form the MCDM problem,the rank of the shor tlisted vendor providers will be done using the fuzzy TOPSIS approach. First,choose the appropriate linguistic variables for the importance squeezet 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 angulate fuzzy number with fuzzy weight for each criterion. Fuzzy weight wj of criterion C j are obtained with regard to DMs opinions. Then the importance of the criteria and the evaluate of alternatives with respect to each criterion and the aggregated rating Xij under criteria C j can be calculated as Wj=1KWj1+Wj2++Wjk xij=1Kxij1+xij2++xijk Wjk is the importance weight of the kth decision maker. xijk is the rating of the kth decision maker. design 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=rijm? n. ri j=(aijcj,bijcj,cijcj) rij=(aj-aij,aj-bij,aj-cij) Next, the weighted normalized fuzzy decision matrix is constructed by V=vijm? n, i=1,2,,m j=1,2,,n Where vij=rij(. )wj After all of these analysis and calculation ,a positive-ideal solution (PIS, A+) and a fuzzy ostracise-ideal solution (NIS,A-) as the criterion are chosen.The best alternative solution should be the closest to the Positive apotheosis Solution (PIS) and the farthest from the Negative Ideal Solution (NIS). A+=(v1*,v2*,,vn*) A-=(v1-,v2-,,vn-) vj*=1,1,1 vj-=0,0,0 target the total distance of each components from the fuzzy positive ideal and negative ideal ? If A and B are two fuzzy numbers as follows, distance between these fuzzy numbers is calculated by equation below A=(a1,b1,c1) B=(a2,b2,c2) Equation DA,B=13a2-a12+b2-b12+c2-c12Given the above description on how to calculate the distance between fuzzy numbers, the distance of components from positive and negative ideas can be derived respectively as di*=j=1nd(vij, vj*), i=1,2,,m di-=j=1nd(vij,vj-), i=1,2,,m In the end,the relative closeness coefficient (CC)of each contractor-project in each criterion can be calculated as CCi=di*di-+di+, i=1,2,,m Stage3 Selecting the best projects and related contractors Select the best projects and related contractors by ranking options based on the descending cci.An alternative with index cci approaching 1 indicates that the alternative is close to the fuzzy positive ideal reference excite and far from the fuzzy negative ideal reference point. A tumid value of closeness index indicates a good performance of the alternative. A fictitious character study The proposed methodology for supplier selection problem, composed of TOPSIS method, consists of ternary Steps (1) Identify the criteria to be used in the model (2) weigh the criteria by using expert views (3) evaluation of alternatives with TOPSIS and determination of the final rank.The case is that of a major company operating in the dairy products field. In the first phase, the project team operated mainly through roundtable discussions on developing their main selection criteria. After identity the criteria attributed under consideration, quin alternatives suppliers are written in the list. There are several criteria need to be considered, and each vendors information under each criteria are collected, calculating each vendors overall rating weight, shown in Table 2. (Mohammad Saeed Zaeri,2010) Finally, the closeness coefficient was calculated to rank alternatives.The results obtained are shown in Table 4 (Mohammad Saeed Zaeri,2010) The order of rating among those vendors is supplier3gt Supplier 4gt Supplier 1gt Supplier2gtSupplier5, the best vendor would be Supplier3. To conclude, the TOPSIS method had several advantages. First, TOPSIS makes it come-at-able to appraise the distances of each candidate from the positive and negative ideal solutions. Second, it allows the great linguistic definition of weights and ratings under each criterion, without the need of cumbersome pairwise comparisons and the risk of inconsistencies.It evaluates the projects and each provider more precisely by expert decision makers in each stage of the whole process. Moreover, the method is very idle to understand and to implement. All these issues are of fundamental importance for a involve field implementation of the methodology by logistics practitioners. However TOPSIS is proved to be insensitive to the number of alternatives and has its worst performance only in case of very limited number of criteria. In order to apply fuzzy TOPSIS to a MCDM problem, selection criteria have to be monotonic.