Quantitative three-way class-specific attribute reducts based on region preservations

Abstract

Attribute reduction of rough set theory is effective for intelligent information processing, and class-specific attribute reducts are beneficial for pattern recognition and rule reasoning. According to three-way decisions, class-specific reducts already have three-way types (namely, positive, negative, and positive-negative) of qualitative optimization, which adhere to classical rough sets. In terms of region preservations, there are no corresponding three-way types of quantitative optimization that match probabilistic rough sets. Thus, this paper constructs and investigates quantitative three-way class-specific attribute reducts based on region preservations. First, the uncertainty/nonmonotonicity of quantitative region change is revealed, and it naturally induces the reduction criteria of quantitative region preservations. Then, quantitative three-way class-specific reducts are constructed, and their basic properties regarding their necessary conditions, attribute cores, and reduct algorithms are achieved. Furthermore, their interrelation regarding equivalence and strengthening/balance are obtained for consistent and inconsistent decision classes, respectively, and their expansions for qualitative three-way class-specific reducts are proved. Finally, relevant concepts and obtained results are effectively verified by decision tables and data experiments. By virtue of sure region preservations, quantitative three-way class-specific attribute reducts robustly extend the existing qualitative three-way class-specific reducts and facilitate the optimal identification and quantitative reasoning of class-specific patterns.