A three-way decisions approach based on double hierarchy linguistic aggregation operators of strict t-norms and t-conorms.

With the massive increase in uncertainty of linguistic information in realistic decision making, there is a great challenge for people to make decisions in the complex linguistic environment. To overcome this challenge, this paper proposes a three-way decisions method based on aggregation operators of strict t-norms and t-conorms under double hierarchy linguistic environment. By mining the double hierarchy linguistic information, strict t-norms and t-conorms are introduced to define the operation rules and their operation examples are also given. Then, the double hierarchy linguistic weighted average (DHLWA) operator and weighted geometric (DHLWG) operator are proposed based on strict t-norms and t-conorms. Besides, some of their important properties are also proved and derived, such as idempotency, boundedness and monotonicity. Next, DHLWA and DHLWG are integrated with three-way decisions to construct our three-way decisions model. Specifically, the double hierarchy linguistic decision theoretic rough set (DHLDTRS) model is constructed by incorporating the computational model of expected loss with DHLWA and DHLWG, which can consider the various decision attitudes from decision makers more adequately. Furthermore, we also propose a novel entropy weight calculation formula to improve the entropy weight method for obtaining the weights more objectively, and integrate grey relational analysis (GRA) method to calculate the conditional probability. Based on the Bayesian minimum-loss decision rules, the solving method of our model is also propounded and the corresponding algorithm is designed. Finally, an illustrative example and experimental analysis are presented, which can validate the rationality, robustness as well as superiority of our method.