Three-way decisions based on some Hamacher aggregation operators under double hierarchy linguistic environment

This paper proposes an approach to linguistic three-way decision making problem with double hierarchy linguistic term evaluation information. Double hierarchy linguistic term set consists of the first hierarchy and second hierarchy linguistic term set, which can describe uncertainty and fuzziness more flexibly. First, the Hamacher operational rules, score function and distance measure of double hierarchy linguistic elements are defined. Next, we construct the double hierarchy linguistic decision-theoretic rough set model. And the conditional probability is calculated based on the double hierarchy linguistic term environment with grey relational analysis, which makes the process of decisions more rational. Then the loss functions are aggregated by the double hierarchy linguistic Hamacher weighted averaging operator, which takes into account different decision attitudes of decision makers. And the results of decision are deduced by the minimum-loss principle. Finally, a case study about the selection of cooperation companies during the COVID-19 is used to demonstrate the practicability of our proposed method.