Approaches to knowledge reduction based on variable precision rough set model

It is proved that for some special thresholds, β lower distribution reduct is equivalent to the maximum distribution reduction reduct, whereas β upper distribution reduCT is equivalents to the possible reduct.

Abstract

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