Attribute Reduction based on Purity Measures in Probabilistic Rough Set Model

Abstract

Attribute reduction is a data analysis method based on rough set theory. It is defined by preserving various measures and/or structures derived from rough set models. In this study, we propose attribute reduction based on purity measures in the probabilistic rough set model. Purity measure is a measure of the uncertainty associated with objects, whether they belong to a target set. We investigate the relationship between conventional attribute reduction methods and purity-based attribute reduction, as well as clarify the relationship between the convexity of purity measures and the monotonicity of reducts.