Quantitative/qualitative region-change uncertainty/certainty in attribute reduction: Comparative region-change analyses based on granular computing

Attribute reduction is a fundamental research theme in rough 'sets and granular computing (GrC). Its scientific construction originally depends on the region-change law. At present, only region-change non-monotonicity/monotonicity is mined in the quantitative/qualitative model. The in-depth region-change truth and its GrC mechanism have significance, especially for follow-up attribute reduction. This paper commences probing region-change essence, mainly from a novel uncertainty/certainty viewpoint. Concretely, we make comparative region-change analyses based on GrC, by resorting to the qualitative Pawlak-Model and quantitative DTRS-Model (the decision-theoretic rough set model). (1) Knowledge-coarsening is investigated to describe attribute deletion. (2) Granule-merging and its region-distribution are studied to probe region-change functions. (3) Region-change is analyzed in Pawlak-Model to mine qualitative region-change certainty and its relevant properties. (4) Region-change is analyzed in DTRS-Model to mine quantitative region-change uncertainty and its relevant properties. (5) Comparative region-change analyses are summarized, and further experiment verification is provided. Knowledge-coarsening and granule-merging establish GrC mechanisms for extensive region-change analyses. Quantitative/qualitative region-change uncertainty/certainty and relevant principles are discovered via DTRS-Model/Pawlak-Model. By virtue of the GrC technology and comparative strategy, this study reveals region-change uncertainty/certainty to deepen region-change non-monotonicity/monotonicity; furthermore, it underlies attribute reduction, especially with regard to quantitative models. (C) 2015 Elsevier Inc. All rights reserved.