A three-way decision model for multi-granular support intuitionistic fuzzy rough sets based on overlap functions

Abstract

Three-way decision-making provides an effective framework for addressing uncertainty, aligning closely with human cognitive decision patterns. This paper proposes a novel three-way decision model based on multi-granular support intuitionistic fuzzy rough sets, integrating n-dimensional overlap and grouping functions. The model constructs optimistic and pessimistic upper and lower approximations to optimize decision rules and introduces score and precision functions for ranking. To validate the model, a consumer decision-making algorithm was developed and applied to empirical data. The results demonstrate that the proposed model effectively narrows decision boundary regions, enhances decision-making precision, and supports decision-making in complex multi-attribute scenarios. This study not only advances rough set theory but also offers practical tools for addressing real-world uncertainty in decision-making.