Ranking Fuzzy Numbers by Defuzzification using Volumes

Fuzzy numbers (FNs) are used to represent uncertain and ambiguous data and are mainly useful in decision-making. Ranking fuzzy numbers is an important concept in fuzzy set theory and has various applications in decision-making, data analysis, artificial intelligence, and optimization problems. To overcome the shortcomings in some of the existing fuzzy ranking methods, in this paper, we introduce a new ranking method for ranking generalized trapezoidal fuzzy numbers (GTrFNs) by a defuzzification technique using a score function defined using the volume of the solid obtained by revolving the left and right inverse membership functions of GTrFN about a vertical line. This score represents the defuzzified value of the GTrFN and is used to rank FNs. The proposed ranking method can rank different types of FNs in an effective manner and can be implemented in real-time applications like multicriteria decision-making and risk analysis.