Comparison of fuzzy numbers based on the probability measure of fuzzy events

In this paper the order of fuzzy numbers are determined based on the concept of probability measure of fuzzy events due to Zadeh, which considers both the mean and dispersion of alternatives and gives two groups of indicesbased on the uniform and the proportional probability distributions.

Abstract

Most approaches for ranking fuzzy numbers proposed in the literature are based on fuzzy sets theory only, and suffer from lack of discrimination and occasionally conflict with intuition. It is true that fuzzy numbers are frequently partial order and cannot be compared. However,this does not alleviate the need for comparison in practical applications. In this paper the order of fuzzy numbers are determined based on the concept of probability measure of fuzzy events due to Zadeh. It considers both the mean and dispersion of alternatives and gives two groups of indices based on the uniform and the proportional probability distributions. The approach is also extended to the comparison of random fuzzy numbers by means of a mean fuzzy number. It is shown that several comparison indices in the literature can be obtained based on the probability present measure approach. Finally some typical examples are used to compare the various different approaches. The different interpretations of the dispersion index under different physical situations are emphasized.