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1 Introduction
Technique for order preference by similarity to ideal solution (TOPSIS) method for solving multiple criteria decision problem (MCDMP) with several alternatives was proposed and developed by [16] Hwang and Yoon (1981). The method is based on the fact that the chosen or most appropriate alternative should have the shortest distance from the positive ideal solution (PIS) and the longest distance from the negative ideal (anti-ideal) solution (NIS). This alternative has the maximum similarity with PIS and minimum similarity with NIS. PIS maximizes the benefit criteria and minimizes cost criteria, whereas NIS minimizes benefit criteria and maximizes cost criteria. [6] Chen and Hwang (1992) transformed this method with the crisp data to the method with the fuzzy data. In last 20 years many authors have participated in development of this method and proposed different modifications. The method has been applied usefully in the practice as a help to the decision makers to solve many problems in different fields of application.
[5] Chen (2000) extended the TOPSIS for group decision making in fuzzy environment. The importance weights of various criteria and ratings of alternatives with respect to these criteria are considered as linguistic variables that are assessed by a decision making group. These variables are transformed into triangular fuzzy numbers according to a table presented in the paper. Final values of fuzzy numbers, that constitute fuzzy decision matrix F and fuzzy weight vector w , are calculated as means of values assessed by the members of the decision group. Normalization of the decision matrix is performed by the linear scale transformation, so that various criteria scales are transformed into a comparable scale. After that, the fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS) are determined. The distances of each alternatives to FPIS and FNIS are calculated by the vertex method, and then corresponding closeness coefficients or relative closeness (RC) of each alternative to these solutions are determined. The alternatives are ranked according to these coefficients, so that alternatives with smaller RC to FPIS and greater RC to FNIS are better ranked. This procedure is relatively simple and has been used and modified by several authors for solving different problems of fuzzy MCDM.
[4] Awasthi et al. (2011) in a similar way...