Region-based quantitative and hierarchical attribute reduction in the two-category decision theoretic rough set model

• An improved type of classification regions and its preservation reduct are proposed.
• The set-region preservation target, property and reduct are studied.
• The double-preservation reduct of set regions and rule consistency is established.
• Hierarchies of three quantitative reducts and two qualitative reducts are explored.

Quantitative attribute reduction exhibits applicability but complexity when compared to qualitative reduction. According to the two-category decision theoretic rough set model, this paper mainly investigates quantitative reducts and their hierarchies (with qualitative reducts) from a regional perspective. (1) An improved type of classification regions is proposed, and its preservation reduct (CRP-Reduct) is studied. (2) Reduction targets and preservation properties of set regions are analyzed, and the set-region preservation reduct (SRP-Reduct) is studied. (3) Separability of set regions and rule consistency is verified, and the quantitative and qualitative double-preservation reduct (DP-Reduct) is established. (4) Hierarchies of CRP-Reduct, SRP-Reduct, and DP-Reduct are explored with two qualitative reducts: the Pawlak-Reduct and knowledge-preservation reduct (KP-Reduct). (5) Finally, verification experiments are provided. CRP-Reduct, SRP-Reduct, and DP-Reduct expand layer by layer Pawlak-Reduct and exhibit quantitative applicability, and the experimental results indicate their effectiveness and hierarchies regarding Pawlak-Reduct and KP-Reduct.