Multi-Attribute Decision-Making Method Based on Interval-Valued $q$ -Rung Orthopair Fuzzy Archimedean Muirhead Mean Operators

Abstract

Interval-valued $q$ -rung orthopair fuzzy sets (IV $q$ -ROFSs), as a generalization of $q$ -rung orthopair fuzzy sets ( $q$ -ROFSs), are the powerful tool for mastering the fuzziness of information. Archimedean t-conorm and t-norm (ATT) consist of t-conorm and t-norm families, which is an important tool for fuzzy sets to generate general operational laws. Meanwhile, the Muirhead mean (MM) operator is a useful aggregation operator that considers the interdependent phenomena among the aggregated arguments. Motivated by those primary characteristics, in this paper, the MM operator to the interval-valued $q$ -rung orthopair fuzzy numbers (IV $q$ -ROFNs) based on the ATT is studied. First, some interval-valued $q$ -rung orthopair fuzzy operational rules are proposed based on ATT. Second, the interval-valued $q$ -rung orthopair fuzzy Archimedean Muirhead mean (IV $q$ -ROFAMM) operator and the interval-valued $q$ -rung orthopair fuzzy weighted Archimedean Muirhead mean (IV $q$ -ROFWAMM) operator are proposed. Third, some desirable properties of the two operators are discussed, and some special cases of the developed operators are investigated. Furthermore, a novel approach based on the IV $q$ -ROFWAMM operator is developed to solve multiple attribute decision-making problem with the interval-valued $q$ -rung orthopair fuzzy information. Finally, a numerical example is given to illustrate the validity of the proposed method and a comparative analysis is conducted to show the superiorities of the method.