Analyzing the ranking method for L–R fuzzy numbers based on deviation degree

Ranking fuzzy numbers based on their left and right deviation degree (L–R deviation degree) has attracted the attention of many scholars recently, yet most of their ranking methods have two systematic shortcomings that are usually ignored. This paper addresses these shortcomings and proves them through mathematical proofs instead of providing counter-examples. Applying our analyses will help other authors avoid some common errors when building their own ranking index functions. We use Asady’s ranking index function (2010) as an example when we present our arguments and proofs and provide fully detailed analyses of two of the ranking index functions herein. Based on these analyses, an algorithm for detecting inconsistencies in ranking results is proposed, and numerical examples are given to illustrate our arguments.

► Two shortcomings in ranking fuzzy numbers based on deviation degree are addressed.
► Mathematical proofs instead of counter examples are given.
► Detailed analysis of two our proposed ranking functions are presented.
► An algorithm for detecting inconsistencies in ranking results is proposed.
► Numerical examples are presented to demonstrate the proposed approach.