Dynamic aggregation operators and Einstein operations based on interval-valued picture hesitant fuzzy information and their applications in multi-period decision making

The traditional picture hesitant fuzzy aggregation operators are generally suitable for aggregating information acquired in the form of picture hesitant fuzzy numbers, but they will fail in dealing with interval-valued picture hesitant fuzzy information. In this paper, we describe the notion of interval-valued picture hesitant fuzzy set and the operational laws of interval-valued picture hesitant fuzzy variables. Moreover, we derive some dynamic interval-valued picture hesitant fuzzy aggregation operators (based on Einstein operators) to aggregate the interval-valued picture hesitant fuzzy information collected at different periods. Some desirable properties of these aggregation operators are discussed in detail. In addition, we develop the approaches to tackle the multi-period decision-making problems, where all decision information takes the form of interval-valued picture hesitant fuzzy information collected at different periods. In an attempt to illustrate the applications of the proposed approaches, two numerical examples are given to measure the impact of Coronavirus Disease 2019 (COVID-19) in daily life and to identify the optimal investment opportunity. Finally, a comparative analysis of the proposed and existing studies are conducted to demonstrate the effectiveness of the proposed approaches. The presented interval-valued picture hesitant fuzzy operations, aggregation operators, and decision-making approaches can widely apply to dynamic decision analysis and multi-stage decision analysis in real life.