Probabilistic approach to rough sets

The article introduces the basic ideas and investigates the probabilistic version of rough set theory. It relies on both classification knowledge and probabilistic knowledge in analysis of rules and attributes. Rough approximation evaluative measures and one-way and two-way inter-set dependency measures are proposed and adopted to probabilistic rule evaluation. A new probabilistic dependency measure for attributes is also introduced and proven to have the monotonicity property. This property makes it possible for the measure to be used to optimize and evaluate attribute-based representations through computation of probabilistic measures of attribute reduct, core and significance factors. (C) 2007 Elsevier Inc. All rights reserved.