A probabilistic approach to rank complex fuzzy numbers

In this paper a probabilistic approach to ranking simple fuzzy numbers is taken and the Mellin transform is introduced to compute the mean and the variance of a complex fuzzy number.

Abstract

Techniques for ranking simple fuzzy numbers are abundant in the literature. However, we lack efficient methods for comparing complex fuzzy numbers that are induced by arithmetic operations. In this paper a probabilistic approach is taken. Membership functions of fuzzy numbers are first converted into probability density functions. The Mellin transform is then introduced to compute the mean and the variance of a complex fuzzy number. The fuzzy number with the higher mean is ranked higher. If the means are equal, the one with the smaller variance is judged higher rank. Two numerical examples and a fuzzy multiple attribute decision analysis are illustrated.