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

There have been many aggregation operators of interval intuitionistic fuzzy values (IVIFVs) for solving multiple criteria decision-making problems with IVIFVs. Each of these operators can work well in its specific context. However, they could generate irrational sorting results because of a few limitations. In this paper, two novel power Muirhead mean operators of IVIFVs under the Dempster-Shafer theory framework which are free of the limitations of existing operators of IVIFVs are presented. The expressions of these operators are first constructed. Then their mathematical properties are studied and proved. After that, a method to solve multiple criteria decision-making problems with IVIFVs is proposed based on the presented operators. Finally, a practical example is introduced to illustrate the application of the proposed method and several qualitative comparisons to some existing operators of IVIFVs are carried out to demonstrate the effectiveness and advantages of the proposed method.