Multiple attribute decision-making method for dealing with heterogeneous relationship among attributes and unknown attribute weight information under q-rung orthopair fuzzy environment

Abstract

A Q‐rung orthopair fuzzy set (q‐ROFS) originally proposed by Yager (2017) is a new generalization of orthopair fuzzy sets, which has a larger representation space of acceptable membership grades and gives decision makers more flexibility to express their real preferences. In this paper, for multiple attribute decision‐making problems with q‐rung orthopair fuzzy information, we propose a new method for dealing with heterogeneous relationship among attributes and unknown attribute weight information. First, we present two novel q‐rung orthopair fuzzy extended Bonferroni mean (q‐ROFEBM) operator and its weighted form (q‐ROFEWEBM). A comparative example is provided to illustrate the advantages of the new operators, that is, they can effectively model the heterogeneous relationship among attributes. We prove that some existing known intuitionistic fuzzy aggregation operators and Pythagorean fuzzy aggregation operators are special cases of the proposed q‐ROFEBM and q‐ROFEWEBM operators. Meanwhile, several desirable properties are also investigated. Then, a new knowledge‐based entropy measure for q‐ROFSs is also proposed to obtain the attribute weights. Based on the proposed q‐ROFWEBM and the new entropy measure, a new method is developed to solve multiple attribute decision making problems with q‐ROFSs. Finally, an illustrative example is given to demonstrate the application process of the proposed method, and a comparison analysis with other existing representative methods is also conducted to show its validity and superiority.

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

“…Ali presented two new approaches for viewing q ‐ROFSs. Liu et al put forward MCDM method for dealing with heterogeneous relationship among attributes and unknown attribute weight information under q ‐ROFS environment. Yager et al investigated the concepts of possibility and certainty as well as plausibility and belief in q ‐ROFS environment.…”

“…The subjective weighting methods place emphasis on the preference information of the experts, while they ignore the objective evaluation information. The objective weight‐determining methods do not take the preference of the decision‐maker into consideration, that is to say, these approaches fail to take the risk attitude of the decision‐maker into account . The feature of our weighting model can have both the subjective information and the objective information.…”

“…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.…”

“…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.…”

Research on arithmetic operations over generalized orthopair fuzzy sets

“…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.…”