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