Ranking fuzzy numbers by volume of solid of revolution of membership function about axis of support

Abstract

It is admissible that fuzzy numbers (FNs) are apt for representing imprecise or vague data in real-world problems. While using FNs in decision-making problems, selecting the best alternative among available alternatives is challenging, and therefore, ranking FNs is essential. We can find different studies in the literature, but to our knowledge, no one attempted to rank FNs using the concept of volume. This paper proposes a new method for ranking generalized fuzzy numbers (GFNs) using the volume of the solid obtained by revolving its membership function (MF) about the x-axis. We calculate the volumes of positive and negative sides along with the centroid of a generalized fuzzy number(GFN) to define the fuzzy number(FN) score. This score represents the defuzzified value of FN, is used to select the best alternative, and overcomes the limitations in some existing methods like ranking FNs having the same centroid, crisp numbers, symmetric fuzzy numbers, and FNs with the same core.