关键词: 决策粗糙集, 属性约简, 属性核

Abstract: Attribute reduction is one of the important research issues in rough set. In Pawlak rough set (PRS), the size of the positive region is monotonic with the increase of the attributes. However, the probabilistic positive region in decision-theoretic rough set (DTRS) may expand with the decrease of the attributes, which is essentially different from that of PRS model and leads to many different definitions of attribute reduction in DTRS model. To address this issue, this paper analyzes the problems of attribute reduction definition in DTRS, and illustrates the relationships among several attribute reductions. This paper also proves that a reduction which keeps the local maximal probabilistic positive regions has larger cost. Finally, this paper points out that a reduction which keeps the positive decision of all objects unchanged takes on the stability and exists the attribute core.

Key words: decision-theoretic rough set, attribute reduction, attribute core