决策粗糙集属性约简算法与属性核研究  

Research on Attribute Reduction Algorithm and Attribute Core in Decision-Theoretic Rough Set

作　　者：钱进 吕萍[1,2] 岳晓冬[3] 

机构地区：[1]江苏理工学院云计算与智能信息处理常州市重点实验室,江苏常州213001 [2]江苏理工学院计算机工程学院,江苏常州213001 [3]上海大学计算机工程与科学学院,上海200444

出　　处：《计算机科学与探索》2014年第3期345-351,共7页Journal of Frontiers of Computer Science and Technology

基　　金：国家自然科学基金Nos.61103067;61142007;常州市云计算与智能信息处理重点实验室项目No.CM20123004;江苏理工学院校基础自然科学资金项目No.kyy 12018;江苏理工学院博士科研启动基金项目No.kyy13003~~

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。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 relation- ships 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.

关 键 词：决策粗糙集 属性约简 属性核 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]