Three-way decision with granular rough sets

By integrating granular computing with rough set theory, granular rough sets enhance the semantics and effectiveness of decision-making through granule-based representations. Existing research has not thoroughly explored the issues of inducing three-way decision rules with granular rough sets, partly due to the challenge of meaningfully describing granules. To address these gaps, this paper proposes a unified framework for three-way decision models based on granular rough sets. Additionally, we introduce a generalized formulation for granule descriptions. It extends traditional representations to include all possible descriptions within a given domain. Through the lens of the proposed framework and granular descriptions, we formulate a three-way decision model in generalized granular rough sets and further demonstrate its instantiation potential across three specific types of granular spaces: quotient spaces, neighborhood-induced granular spaces, and maximal-clique-induced granular spaces. The effectiveness of the proposed models is illustrated through examples using set-valued information tables and experiments on real-world datasets. The results show that the proposed models have good performance and practical applicability.