A novel three-way decision approach under hesitant fuzzy information

The paper explores a novel way to solve the multi-attribute decision-making issues under the hesitant fuzzy environment (HF-MADM) with three-way decision (3WD) theory. Firstly, according to the nature of the relative loss function (RLF), the RLF under the hesitant fuzzy (HF) environment is defined. Then, according to the practical significance of the loss function, this paper establishes the relationship between the loss function and the evaluation value. At the same time, considering that the HF-MADM has multiple attributes and multiple evaluation values, we provide an aggregated loss function via the hesitant fuzzy weight average (HFWA) operator to reflect the overall loss of the alternative. We establish the mixed information table (HF-MADMRLF) based on the overall loss function. Secondly, based on an outranking function and a distance from the positive ideal (PI) solution, this paper defines an estimation on the conditional probability method. Finally, we utilize the presented method to solve actual medical diagnosis of pneumonia (MDP) issue, and prove the validity and applicability of the method through comparison with several representative methods and experimental evaluations.