Selection method by fuzzy set theory and preference matrix

Abstract

In fuzzy decision making problems, fuzzy ranking is one of the most preferred aeras. The aim of this paper to develop a new ranking method which is reliable and doesnot need tremendous arithmetic calculations. Also it can be used for all type of fuzzy numbers which are represented as crisp form or in linguistic form. Fuzzy multi criteria decision making commonly employs methods such as ordering method,Fuzzy Analytic Hierarchy Process [FAHP], Fuzzy Technique for Order Preference by Similarity to Ideal Solution [FTOPSIS]and hybrid method. The FAHP commonly uses triangular fuzzy numbers and trapezoidal fuzzy numbers while the FTOPSIS method identifies the best alternative as the one that is nearest to the positive ideal solution and farthest to the negative ideal solution. Although both these methods have been widely used, they have their drawbacks. The accuracy of these methods decreases as the number of alternative increases i.e. the more complex the problem, less the accuracy and all the methods have many computations. In order to overcome this problem, we propose a method which is a combination of method of Blin and Whinston(1973) and method of Shimura(1973). This way the advantages of both the methods may be utilized to arrive at a decision that involves vague data. In this  paper, we use the concept of preference matrix to find the membership grades and calculate the ranking.

Keywords: Fuzzy set, preference matrix, multi person decision making, multi criteria decision making(MCDM), relativity function matrix.