A Hesitant Fuzzy Rough Set-Based Three-Way Decision Model and Its Application in Infectious Disease Diagnosis

Hesitant fuzzy information systems are effective tools for expressing uncertain information. How to solve decision-making problems in hesitant fuzzy information systems is the focus of this paper. Three-way decision and hesitant fuzzy rough sets are effective tools for solving uncertainty problems. Therefore, an improved three-way decision model based on hesitant fuzzy rough sets is developed in hesitant fuzzy information systems, which extends existing models to provide more objective and reliable decision actions for alternatives. Firstly, an attribute-oriented hesitant fuzzy state set is introduced, and combined with generalized hesitant fuzzy rough set theory to rationally estimate the conditional probability that alternatives belong to the state set. Secondly, aggregated relative loss functions are defined in hesitant fuzzy information systems by combining objective attribute weights and relative loss functions on alternatives under different attributes. Thirdly, expected losses on alternatives are acquired by combining conditional probabilities and aggregated relative loss functions, which allow alternatives to be reasonably categorized and ranked. Finally, the practicality of the proposed model is validated by an example study, and compared with several representative methods based on quantitative and qualitative analysis.