Fuzzy Topsis Method

wooly-minded TOPSIS regularity This is an approach establish on the TOPSIS technique (Technique for Order gustation by Similarity to nonpareil Solution) and the fuzzed set theory. The TOPSIS system is based on the concept that the optimum option has the least distance from the compulsive nonpareil ancestor. It is a unidimensional countting 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 take to solve MCDM problems in many varied fields. Because conclusion entropy is uncertain instead of certain in most environments, only extension for group finale reservation problems on a lower floor hairy environment was print by Cheng(2000),known as Fuzzy TOPSIS. The endurance of the third-party supplier is a typical MCDM problem. In this method firstly we screen bug out providers that produce not minimal qualifications by the filling criteria.Then in timacy coefficient of declarers to to each one(prenominal) intention will be computed by Fuzzy TOPSIS method and finally these coefficients as sure-fire indicators for each provider will be fed in to a linear programming to select most advantageous bug outs and providers with approve to the constraints. The stages are described buffet Stage1 Eliminate contractors that havent minimal qualifications. For the purpose of outline, woof criteria need to be rationally selected at first. on that point are a spile of researches with respect to the ratiocination criteria for evaluating the supplier.Such as the believe of Dickson(1966), Ellram (1990),Weber et al. (1991), ,Grupe (1997), and Akomode et al. (1998). According to an empirical survey, the top quad woof criteria are responsiveness to run requirements, quality of management, track record of honest importance, and ability to provide measure-added services. The less all important(p) woof criteria are listed in a d escending distinguish as beneath low cost, specific channel expertise, cognition of market, personal relationship with key contacts, willingness to espouse take chances, investment in state-of- art technologies, size of it 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 summately patience specific and based on each case and the criteria are changed and replaced. Then opinions of decision makers on criteria were mass 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 computation closeness coefficient (CC) for each project by logy TOPSIS method So by and by we have obtained the important military grade criteria and the fitting pro vider quite a littledidates to form the MCDM problem,the ranking of the shortlisted vendor providers will be done use the muddled 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 measuring by DM, using linguistic variables.Convert these evaluation into angulate woolly-headed numbers with hairy 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 pass judgment 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. 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=rijm? n. rij=(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- angel solution (PIS, A+) and a fuzzy negative-ideal solution (NIS,A-) as the criterion are chosen.The ruff alternative solution should be the closest to the Positive nonpareil 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 Calculate 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 amidst 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 dis tance 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 to contractors Select the best projects and related contractors by ranking options based on the descending cci.An alternative with index cci orgasm 1 indicates that the alternative is close to the fuzzy positive ideal reference post and far from the fuzzy negative ideal reference point. A large value of closeness index indicates a comfortably transaction of the alternative. A case field of force The proposed methodological analysis for supplier selection problem, represent of TOPSIS method, consists of three 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 an d 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 round table discussions on developing their main selection criteria. After identity the criteria attributed under consideration, flipper alternatives suppliers are written in the list. There are several criteria need to be considered, and each vendors information under each criteria are collected, scheming each vendors boilers suit 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 possible to appraise the distances of each candidate from the positive and negative ideal solutions. Second, it allows the straight 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 only by expert decision makers in each stage of the whole process. Moreover, the method is rattling easy to understand and to implement. both these issues are of fundamental importance for a direct 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.