Some Intuitionistic Cubic Fuzzy Muirhead Mean Operators with Their Application to Multicriteria Decision Making

Abstract

Intuitionistic cubic fuzzy sets (ICFSs), as a hybrid fuzzy set consisting of interval-valued fuzzy sets and intuitionistic fuzzy sets, can deal with the uncertainty of information in decision problems more comprehensively. Muirhead mean (MM) operators can deal with the correlation between attributes in decision problems more realistically. However, there has been no research on MM operators under intuitionistic cubic fuzzy sets so far. In this study, some new operators are proposed under the intuitionistic cubic fuzzy set. It contains the intuitionistic cubic fuzzy MM (ICFMM) operator, intuitionistic cubic fuzzy weighted MM (ICFWMM) operator, intuitionistic cubic fuzzy dual MM (ICFDMM) operator, and intuitionistic cubic fuzzy dual weighted MM (ICFDWMM) operator. Their proof procedure, properties, and proof of properties are given. Two MCDM decision models based on ICFWMM and ICFDWMM operators are proposed, and the proposed decision models are applied to supplier selection, and the better reliability and accuracy of the proposed decision methods in this study are verified through comparative analysis with existing methods.