Ranking Fuzzy Numbers with Unified Integral Value and Comparative Reviews
DOI:
https://doi.org/10.3329/jsr.v14i1.53735Abstract
Fuzzy numbers represent ambiguous numeric values; therefore, it is difficult to rank them according to their magnitude. In making decisions, it is important to rank the fuzzy numbers. Since fuzzy numbers in a fuzzy environment often measure alternatives, a comparison of these fuzzy numbers is, in fact, a comparison of alternatives. There are a lot of different types of methods for ranking fuzzy numbers that exist in the literature. Still, there is no single method superior to all others regarding discrimination and consistency. This paper proposes a method for ranking fuzzy numbers with a unified integral value that multiplies two discriminatory components, the mode area integral and a linear sum of the absolute values of the integrals of the left and the right limits of alpha-cut of the normalized form of a fuzzy number. The method can rank two or more fuzzy numbers simultaneously, regardless of their linear or nonlinear membership functions. Furthermore, the unified integral value consistently ranks fuzzy numbers and their images and symmetric fuzzy numbers with the same altitude. Various types of fuzzy numbers are used in examples for comparative studies and investigations.
Downloads
27
32
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
© Journal of Scientific Research
Articles published in the "Journal of Scientific Research" are Open Access articles under a Creative Commons Attribution-ShareAlike 4.0 International license (CC BY-SA 4.0). This license permits use, distribution and reproduction in any medium, provided the original work is properly cited and initial publication in this journal. In addition to that, users must provide a link to the license, indicate if changes are made and distribute using the same license as original if the original content has been remixed, transformed or built upon.