Ordering Fuzzy Numbers with Weighted Mean Values and Their Application to Multi-Criteria Decision-Making Problem

Abstract

The most important aspect of fuzzy numbers is their ordering, which ensures a wide range of their applications in professional life and many academic applied models like linguistic decision-making and fuzzy risk analysis. Even though many researchers have presented various methods, there is still a lot of interest and scope for studies to address the weakness of methods. This paper proposes an approach for ordering generalized fuzzy numbers using weighted mean values (centroid values) of the left and the right fuzziness regions and exponential values of the altitude of the fuzzy number. The proposed method can order two or more fuzzy numbers simultaneously, irrespective of their linear or non-linear membership functions. Furthermore, the proposed method consistently orders the symmetrical fuzzy numbers, the partnered image of the fuzzy number, and the fuzzy numbers that depict the compensation of areas. The advantages of the proposed approach are demonstrated through numerical examples with various types of fuzzy numbers and comparisons with the existing techniques published in the literature. Finally, the proposed method is effectively applied to solve a linguistic multi-criteria decision-making problem related to the stock market.