Approaches to knowledge reduction based on variable precision rough set model

This paper deals with approaches to knowledge reduction based on variable precision rough set model. The concepts of beta lower distribution reduct and beta upper distribution reduct based on variable precision rough sets (VPRS) are first introduced. Their equivalent definitions are then given, and the relationships among beta lower and beta upper distribution reducts and alternative types of knowledge reduction in inconsistent systems are investigated. It is proved that for some special thresholds, beta lower distribution reduct is equivalent to the maximum distribution reduct, whereas beta upper distribution reduct is equivalent to the possible reduct. The judgement theorems and discernibility matrices associated with the beta lower and beta upper distribution reducts are also established, from which we can obtain the approaches to knowledge reduction in VPRS. (C) 2003 Elsevier Inc. All rights reserved.