A new approach to cubic q-rung orthopair fuzzy multiple attribute group decision-making based on power Muirhead mean

The q-rung orthopair fuzzy sets (q-ROFSs) have been proved to be an efficient tool in expressing decision makers’ (DMs) evaluation values in multiple attribute group decision-making (MAGDM) procedure. To more effectively represent DMs’ evaluation information in complicated MAGDM process, this paper proposes a new tool, called cubic q-rung orthopair fuzzy sets (Cq-ROFSs), based on the combination of q-ROFSs with interval-valued q-ROFSs. Then, we investigate MAGDM problems in which DMs’ preference information is given in terms of cubic q-rung orthopair fuzzy numbers. First, the definition, operations and comparison method of Cq-ROFSs are introduced. Second, to effectively aggregate cubic q-rung orthopair fuzzy information we propose the cubic q-rung orthopair fuzzy power average operator, the cubic q-rung orthopair fuzzy power Muirhead mean operator as well as their weighted forms. We illustrate the powerfulness and flexibility of the proposed operators in fusing cubic q-rung orthopair fuzzy decision-making information. Third, on the basis of the proposed operators we give the main steps of a novel cubic q-rung orthopair fuzzy MAGDM method. We utilize the method to solve real MAGDM problems to prove its effectiveness and validity. Finally, we explain why DMs should choose our proposed method rather than some others through comparison analysis.