Optimistic Ranking Pessimistic Ranking and Neutral Ranking of Generalized Fuzzy Numbers Using the Integral Mean Value

Abstract

Fuzzy numbers ranking methods are one of the important tools for decision-makers in real-world problems. Often fuzzy numbers may not be normal, which are called generalized fuzzy numbers (G-fuzzy numbers). In this work, a simple and efficient method is given to rank fuzzy numbers. For every given G-fuzzy number we use interval arithmetic to assign two suitable intervals that are called pessimistic and optimistic expected ranking intervals, respectively. Since a decision-maker may be optimistic, pessimistic, or neutral, we use an index to choose a point of these intervals to rank G-fuzzy numbers according to the point of view of decision-makers. In this manner, our method can be used to rank all arbitrary G-fuzzy numbers without attention to certain cases. Some examples are given to compare the proposed method with other methods.