A family of similarity measures for q‐rung orthopair fuzzy sets and their applications to multiple criteria decision making

Abstract

One worthwhile way of expressing imprecise information is the q-rung orthopair fuzzy sets (q-ROFSs), which extend intuitionistic fuzzy sets and Pythagorean fuzzy sets. The main goal of this contribution is to further extend the concept of similarity measure for q-ROFSs, which not only endows the similarity framework with more ability to create new ones but also inherits all essential properties of a logical similarity measure. This contribution proposes a class of novel similarity measures for q-ROFSs by drawing a general framework of existing q-ROFS similarity and q-ROFS distance measures. These q-ROFS similarity measures enable us to overcome the theoretical drawbacks of the existing measures in the case where they are used individually. In the application part of the contribution, a pattern recognition problem on classification of building materials with a number of known building materials is reconsidered. The study of this particular case shows that the proposed family of similarity measures consistently classify the unknown building material pattern with the same known building material pattern. Then, an experimental case study regarding a problem of classroom teaching quality is re-examined for the comparison of the performance of proposed similarity measures against the existing ones. The salient features of the proposed similarity measures in comparison to the existing qROFS similarity measures, are as follows: (i) a number of existing q-ROFS similarity measures are inherently correlation coefficients, and they satisfy only a limited number of essential properties of a comprehensive similarity measure; (ii) several existing q-ROFS similarity measures lead sometimes to nonlogical results, more specifically, to the same maximum similarity value for different q-ROFSs; (iii) a variety of existing q-ROFS similarity measures depend on subjective parameters, which either hinder their application in practice or increase their computational cost. In brief, following this direction of research, we will prove the superiority of the developed similarity measures over the existing ones from both theoretical and experimental viewpoints.