Exploration of rough approximation operators with supervised justifiable granularity principle

Rough set theory is a representative granular computing model that has received widespread attention. Rough approximation operators (RAOs) serve as foundational components in rough set models, leveraging information granules to approximate abstract concepts. The justifiable granularity principle (JGP) is one of the fundamentals in granular computing, and has achieved great success in the design and evaluation of information granules. Within this context, this study investigates RAOs based on the JGP in classification learning. First, the limitations of two types of popular RAOs, namely probabilistic and fuzzy RAOs, are analyzed from a classification learning perspective. It is concluded that different samples lack discrimination w.r.t. the decision classes in these RAOs. Subsequently, the supervised JGP (SJGP) is proposed. The relative coverage and relative specificity of information granules are formulated w.r.t. the decision classes. These are integrated into existing RAOs to address the challenges. Finally, a new type of reduct is introduced, and a unified framework for heuristic algorithms is also developed correspondingly. The proposed RAOs are applied to attribute reduction. Experimental results demonstrate the reasonableness and superiority of integrating SJGP into RAOs.