Three-way weighted entropies and three-way attribute reduction

Abstract

Rough set theory (RS-Theory) is a fundamental model of granular computing (GrC) for uncertainty information processing, and information entropy theory provides an effective approach for its uncertainty representation and attribute reduction. Thus, this paper hierarchically constructs three-way weighted entropies (i.e., the likelihood, prior, and posterior weighted entropies) by adopting a GrC strategy from the concept level to classification level, and it further explores three-way attribute reduction (i.e., the likelihood, prior, and posterior attribute reduction) by resorting to a novel approach of Bayesian inference. From two new perspectives of GrC and Bayesian inference, this study provides some new insights into the uncertainty measurement and attribute reduction of information theory-based RS-Theory.