A three-way decision method based on fuzzy rough set models under incomplete environments

Abstract The paper primarily explores the applicability of three-way decision (TWD) to multi-attribute decision-making (MADM), and establishes a new three-way multi-attribute decision-making (TW-MADM) method under an incomplete environment. For the sake of making rational decisions for MADM problems with fuzzy values, fuzzy rough set models are first utilized to investigate a new TWD model. By taking into account the hesitation degree of each evaluation value, a data-driven method to determine the relative loss functions is presented. Moreover, a new conditional probability calculation method is put forth via the information granularity of each object. In light of the above statement, a novel TWD model with three strategies is proposed. Afterwards, the arithmetic mean method is adopted for patching the lost data to effectively address incomplete MADM problems. Given the uncertainty of the patched data and real data, a new TW-MADM method as well as a corresponding MADM algorithm is designed. By several comparative analysis and experimental analysis, the feasibility, effectiveness, superiority and stability of the method are demonstrated. In addition, the results show that the presented method with optimistic strategies is more viable and stable than the method with compromise and pessimistic strategies.