A New Fuzzy Positive and Negative Ideal Solution for Fuzzy TOPSIS

This paper presents a fuzzy multiple criteria decision making (FMCDM) problem with the Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) based on the new concept of positive and negative ideal solution. Whereas decision making is a process which accuracy of data play major role to select the best alternative, considering decision making problems in fuzzy environments motivate the authors to search in this field. Triangular fuzzy numbers (TFN) among decision making process are used to evaluate the weighted different alternatives versus various criteria and a fuzzy group weight is made by different experts. In this paper, additionally, a new fuzzy distance formula is applied to compute distance between each alternative and positive as well as negative ideal solution. There is a flexibility to consider general fuzzy numbers (such as triangular, trapezoidal, interval), though. Then, new fuzzy TOPSIS to determine the ranking order of the alternatives is also presented. Finally, a numerical example from the literature is solved to demonstrate applicability of the proposed model. The comparison of illustrated algorithm with the three methods in the literature on various examples proved the efficiency of our decisions. . Key-Words: TOPSIS, Fuzzy Numbers, Fuzzy Distance, Positive Ideal Solution, Negative Ideal Solution.