Interval-valued intuitionistic fuzzy hybrid weighted averaging operator based on Einstein operation and its application to decision making

The notion of interval-valued intuitionistic fuzzy set IVIFS is a generalization of that of Atanassov's intuitionistic fuzzy set AIFS. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. In this paper, we define some Einstein operations on IVIFS and develop three arithmetic averaging operators, such as the interval-valued intuitionistic fuzzy Einstein weighted averaging IVIFWAe operator, interval-valued intuitionistic fuzzy Einstein ordered weighted averaging IVIFOWAe operator, and interval-valued intuitionistic fuzzy Einstein hybrid weighted averaging IVIFHWAe operator, for aggregating interval-valued intuitionistic fuzzy information. The IVIFHWAe operator generalizes both the IVIFWAe and IVIFOWAe operators. Moreover, we establish various properties of these operators and derive the relationship between the proposed operators and the exiting aggregation operators. Finally, we apply the IVIFHWAe operator to multiple attribute decision making with interval-valued intuitionistic fuzzy information.

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