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

摘要： 属性约简是粗糙集理论的重要研究内容之一。在Pawlak粗糙集模型中，正区域大小随着属性增多而变大，呈现单调性。然而，在决策粗糙集模型中，概率正区域与属性集之间不具有单调性，从而产生各种属性约简定义。为此，深入研究了决策粗糙集属性约简问题，阐述了几种约简定义之间的关系，证明了保持局部最大概率正区域的约简具有较大的代价，指出了保持所有对象的正决策不变的约简呈现稳定性和存在属性核。

关键词: 决策粗糙集, 属性约简, 属性核