A Novel Decision-Making Method for Selecting Superintendent Based on a Q-Rung Dual Hesitant Fuzzy Power Partitioned Bonferroni Mean Operator

Abstract

The Q-rung dual hesitant fuzzy (q-RDHF) set is famous for expressing information composed of asymmetry evaluations, because it allows for several possible evaluations in both the membership degree and non-membership degree. Compared with some existing extended fuzzy theories, the q-RDHF set is more superior and flexible because it can handle asymmetric assessments. In order to assemble the evaluation information expressed by q-RDHF elements, this paper aims to propose new operators to integrate q-RDHF elements. The partitioned Bonferroni mean (PBM) operator is well-known for its advantages in coping with the inhomogeneous relationship between asymmetry input arguments. In this paper, we combine the PBM operator with the power average operator, and propose a family of q-RDHF power PBM operators. Some theorems and special cases for the new proposed operators are discussed. Furthermore, we provide a general framework for dealing with multiple attribute decision-making (MADM) problems using the novel proposed method. To better show the calculation details, a numerical case study of the application of the proposed method in a superintendent selection problem is introduced. In addition, we utilize the proposed method to compare it with some existing methods in order to show its flexibility and superiority. The results show that our method is much more advantageous when considering flexible actual situations. Finally, the conclusion is given. The main contributions of this study are to propose an appropriate method to solve unbalanced and asymmetry information in a q-RDHF environment, and to apply it into a realistic superintendent selection problem.