Knowledge Reduction in Set-Valued Decision Information System

Abstract

Reduction is one of the key problem in rough set theory due to its applications in data mining, rule induction, classification, etc.. In this paper the reductions for a set-valued decision information system(DIS) are studied. The judgment theorem and the discernibility matrix of the generalized decision reduct in a set-valued DIS are given, and the relationships among the generalized decision reduct and alternative types of knowledge reduction in set-valued DIS are investigated. It is proved that the reduct in the consistent set-valued DIS is equivalent to the generalized decision reduct, and the possible reduct in the inconsistent set-valued DIS is equivalent to the generalized decision reduct. The judgment theorem and the discernibility matrix associated with the possible reduct are also established.