Interval-valued hesitant fuzzy Einstein prioritized aggregation operators and their applications to multi-attribute group decision making

Interval-valued hesitant fuzzy information aggregation plays an important role in interval-valued hesitant fuzzy set theory, which has received more and more attention in recent years. In this paper, we investigate interval-valued hesitant fuzzy multi-attribute group decision-making problems in which there exists a prioritization relationship among the attributes. Firstly, we introduce some Einstein operational laws on interval-valued hesitant fuzzy sets, and discuss some relations of these operations. Then, we develop two interval-valued hesitant fuzzy prioritized aggregation operators with the help of Einstein operations, such as the interval-valued hesitant fuzzy Einstein prioritized weighted average (IVHFEPWA) operator and the interval-valued hesitant fuzzy Einstein prioritized weighted geometric (IVHFEPWG) operator, whose desirable properties are investigated in detail. We further analyze the relationship between these proposed operators and the existing interval-valued hesitant fuzzy prioritized aggregation operators. Moreover, an approach to interval-valued hesitant fuzzy multi-attribute group decision making is given on the basis of the proposed operators. Finally, a numerical example is provided to demonstrate their effectiveness.