覆盖粗糙集属性约简的新算法  

A New Attribute Reduction Algorithm of Covering Rough Sets

作　　者：杨田[1] 伍秀华[1] 王玉芳[2] 

机构地区：[1]中南林业科技大学理学院,湖南长沙410004 [2]荆楚理工学院数理学院,湖北荆门448000

出　　处：《模糊系统与数学》2013年第2期183-190,共8页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11201490);湖南省科技厅科技计划项目(2011FJ3152;2012FJ3145)

摘　　要：覆盖广义粗糙集是Pawlak粗糙集的重要推广,其属性约简是粗糙集理论中最重要的问题之一。Tsang等基于一种生成覆盖设计了覆盖信息系统属性约简算法,但并未明确指出其适用的覆盖粗糙集类型。在本文中,我们首先指出Tsang的属性约简算法适用的覆盖粗糙集是第五,第六和第七类。其次,我们通过建立覆盖与自反且传递的二元关系之间的等价关系,提出了一种时间复杂度更低的属性约简算法,并证明了本文中的属性约简方法就是Wang等所提出的一般二元关系属性约简的特例。本文不仅提出了属性约简的简化算法,还首次建立起覆盖属性约简与二元关系属性约简之间的联系,具有理论和实际的双重意义。As an essential extention of Pawlak rough sets, covering rough sets enjoys its unique advantages in various areas. The attribute reduction of covering rough set models is one of the most important technique in rough sets. Tsang et. al. design an attribute reduction algorithm of covering rough sets, without pointing out which models are fit for. In this paper, we show that the attribute reduction algorithm is fit for the fifth, the sixth and the seventh models. Further more, a covering can be represented by a reflexive and transitive binary relation equivalently. As a result, the algorithm designed by Tsang et al. is proved to he a special case of the attribute reduction technique proposed by Wang et al. Most importantly, a simplified approach to attribute reduction of covering rough sets is proposed and the gap between attribute reduction base on covering and those based on binary relation is bridged.

关 键 词：粗糙集 粒计算 覆盖 信息系统 属性约简 二元关系 

分 类 号：O189[理学—数学] TP18[理学—基础数学]