A revised method for ranking fuzzy numbers using maximizing set and minimizing set

Abstract

A large number of methods have been proposed for ranking fuzzy numbers in the last few decades. Nevertheless, none of these methods can always guarantee a consistent result for every situation. Some of them are even non-intuitive and not discriminating. Chen proposed a ranking method in 1985 to overcome these limitations and simplify the computational procedure based on the criteria of total utility through maximizing set and minimizing set. However, there were some shortcomings associated with Chen’s ranking method. Therefore, we propose a revised ranking method that can overcome these shortcomings. Instead of considering just a single left and a single right utility in the total utility, the proposed method considers two left and two right utilities. In addition, the proposed method also takes into account the decision maker’s optimistic attitude of fuzzy numbers. Several comparative examples and an application demonstrating the usage, advantages, and applicability of the revised ranking method are presented. It can be concluded that the revised ranking method can effectively resolve the issues with Chen’s ranking method. Moreover, the revised ranking method can be used to differentiate different types of fuzzy numbers.