A decision-theoretic fuzzy rough set in hesitant fuzzy information systems and its application in multi-attribute decision-making

Abstract

Decision-theoretic rough sets (DTRSs) as a classic model of three-way decisions have been widely applied in the field of risk decision-making. Considering situations where experts hesitate among several evaluation values, hesitant fuzzy sets, as a new generalization of fuzzy sets, can describe uncertain information flexibly in the decision-making process. In this paper, we propose a decision-theoretic fuzzy rough set (DTFRS) model in hesitant fuzzy information systems and discuss its application in multi-attribute decision-making (MADM). More specifically, we first define a novel fuzzy binary relation between two objects by using the hesitant fuzzy distance function. Then, we study the calculations of the fuzzy similarity class and the conditional probability. At the same time, based on the connection between the loss functions and the attribute values, we develop a data-driven calculation method of the relative loss functions. With these discussions, we construct a DTFRS model in hesitant fuzzy information systems and explore the related decision-making mechanism. Furthermore, a three-way decision method based on the proposed DTFRS model is established to handle MADM problems in the context of a hesitant fuzzy environment. The established method not only takes the decision risk into consideration, but also instructs us how to choose the action for each alternative and gives its corresponding semantic explanation. An illustrative example of the stock investment problem is presented to verify the efficacy of our method. Finally, we take a sensitivity analysis and a comparison analysis to show the established method’s performance and characteristics.