A three-way decision combining multi-granularity variable precision fuzzy rough set and TOPSIS method

This study proposed an innovative fuzzy rough set model to address multi-attribute decision-making problems. Initially, we introduced a novel model of multi-granularity variable precision fuzzy rough sets, which included three foundational models. This model was demonstrated to possess favorable algebraic and topological properties, and particularly noteworthy the comparable property. Subsequently, by integrating the novel model with the TOPSIS method, a novel three-way decision model was proposed. Within this framework, three fundamental models of multi-granularity variable precision fuzzy rough sets were applied in three methods to construct relative loss functions. This resulted in a three-way decision model with three distinct strategies. Finally, we implemented the proposed three-way decision model for risk detection in maternal women. Several experiments and comparisons were conducted to validate the effectiveness, stability, and reliability of our proposed approach. The experimental results indicated that the proposed method accurately classified and ranked maternal women. Overall, our approach offered multiple strategies and fault tolerance and was found to be effective for a large amount of data. •A multi-granularity variable precision fuzzy rough set with three basic models is introduced.•A three-way decision model with three strategies, regarded as a wide three-way, is proposed.•The three-way decision model, applied to maternal health risks, enables simultaneous classification and ranking.