Power Muirhead mean operators of interval-valued intuitionistic fuzzy values in the framework of Dempster–Shafer theory for multiple criteria decision-making

Multiple criteria decision-making (MCDM) based on interval intuitionistic fuzzy value (IVIFV) is a process of aggregating decision criteria represented by multiple interval-valued intuitionistic fuzzy numbers to select the optimal alternative. Among them, an aggregation operator is an indispensable tool, and the properties of an aggregation operator directly affect the decision results. Existing aggregation operators based on IVIFV have satisfactory results in eliminating the correlation between criteria and removing the influence of outliers on the results. However, there are some unreasonable results due to some undesired properties of IVIFVs. In this paper, IVIFV operation under the Dempster-Shafer theory (DST) framework is applied to combine the power average and Muirhead mean operators and interval intuitionistic fuzzy power Muirhead mean operators under DST framework are presented. Then a method based on the presented operators for MCDM problems is proposed. Finally, a set of numerical experiments are conducted to demonstrate the proposed method. The experimental results suggest that the proposed method not only retains the robustness of the power average operator and the capability of the Muirhead mean operator, but also eliminates a shortcoming that existing interval intuitionistic fuzzy operators cannot handle the case where the weights are in IVIFVs.