Someq-Rung Orthopai Fuzzy Bonferroni Mean Operators and Their Application to Multi-Attribute Group Decision Making

Abstract

In the real multi‐attribute group decision making (MAGDM), there will be a mutual relationship between different attributes. As we all know, the Bonferroni mean (BM) operator has the advantage of considering interrelationships between parameters. In addition, in describing uncertain information, the eminent characteristic of q‐rung orthopair fuzzy sets (q‐ROFs) is that the sum of the qth power of the membership degree and the qth power of the degrees of non‐membership is equal to or less than 1, so the space of uncertain information they can describe is broader. In this paper, we combine the BM operator with q‐rung orthopair fuzzy numbers (q‐ROFNs) to propose the q‐rung orthopair fuzzy BM (q‐ROFBM) operator, the q‐rung orthopair fuzzy weighted BM (q‐ROFWBM) operator, the q‐rung orthopair fuzzy geometric BM (q‐ROFGBM) operator, and the q‐rung orthopair fuzzy weighted geometric BM (q‐ROFWGBM) operator, then the MAGDM methods are developed based on these operators. Finally, we use an example to illustrate the MAGDM process of the proposed methods. The proposed methods based on q‐ROFWBM and q‐ROFWGBM operators are very useful to deal with MAGDM problems.

Research on arithmetic operations over generalized orthopair fuzzy sets

“…Note that if , is an intuitionistic fuzzy number (also called an intuitionistic fuzzy value) and if , is a Pythagorean fuzzy number . Following these terminologies, a ‐ROMG is also called a ‐rung orthopair fuzzy number . To avoid confusion with the term fuzzy number , we still use the original name proposed by Yager in this paper.…”

“…Specially, Yager et al developed the OWA and Choquet aggregation operations on ‐ROFSs. Along this line of research, Liu and his colleagues introduced the weighted averaging/geometric operation, (weighted, geometric) Bonferroni mean operation, (weighted) extended Bonferroni mean operation, (weighted) Archimedean Bonferroni mean operation, power (weighted) Maclaurin symmetric mean operation, and (weighted) Heronian mean operation on ‐ROFSs. Wei et al further put forward the generalized (weighted) Heronian mean operation and (weighted) geometric Heronian mean operation for ‐ROFSs.…”

Research on the assessment of classroom teaching quality with q ‐rung orthopair fuzzy information based on multiparametric similarity measure and combinative distance‐based assessment

“…Due to the shortcomings (counterintuitive phenomena, higher computational complexity) of the existing decision‐making algorithms for q ‐ROFSs, they may be difficult for decision‐makers to select convincible or optimal alternatives. As a consequence, the aim of this paper is to deal the two challenges mentioned above by developing two MCDM approaches to managing evaluation information for q ‐ROFSs, which not only have a lower computational complexity, but also can achieve an optimal alternative out of counterintuitive phenomena.…”

“…The effect of the four parameters () on the ordering of the alternatives are presented. The new score function for q ‐rung orthopair fuzzy number ( q ‐ROFN) is put forward for dealing the comparison problem Two proposed algorithms with some existing algorithms are compared by some examples. Their objective evaluation is carried out, and the methods which maintain consistency of their results are chosen.…”

Multi‐attribute group decision‐making methods based on q‐rung orthopair fuzzy linguistic sets

“…Liu and Wang developed some weighted average operators, weighted geometric operators, power Maclaurin symmetric mean operators, and archimedean Bonferroni operators to handle MAGDM problems based on q‐ROFS. Liu and Liu developed some Bonferroni mean operators based on q‐ROFS to solve MAGDM problems. Wei et al proposed some generalized Heronian mean operators based on q‐ROFS and discussed some interesting properties in MADM.…”