几种不同属性约简的比较研究  

Comparative Research of Different Attribute Reduction Definitions

作　　者：徐章艳[1] 杨炳儒[1] 宋威[1] 侯伟[1] 

机构地区：[1]北京科技大学信息工程学院

出　　处：《小型微型计算机系统》2008年第5期848-853,共6页Journal of Chinese Computer Systems

基　　金：国家自然科学基金重点项目(6983500160463003)资助;北京市自然科学基金项目(4022008)资助;广西教育厅科研项目(200626)资助

摘　　要：为研究基于HU差别矩阵、信息熵、分布、最大分布、近似和正区域的属性约简的关系,首先构造了HU简化差别矩阵;构造了基于正区域的简化差别矩阵,证明了基于该简化差别矩阵的属性约简与基于正区域的属性约简是等价的.然后利用HU简化差别矩阵证明了:若B满足φ≠mij∈M使得mij∩B≠φ(其中M表示HU的差别矩阵),则B一定满足H(D|B)=H(D|C);利用基于正区域的简化差别矩阵和基于近似约简的简化差别矩阵证明了:若B是近似协调集,则B一定满足POSB(D)=POSC(D).结合已有的研究结果,得出了上述不同属性约简之间的关系.To study the relationships of the attribute reduction definitions based on Hu＇s discernibility matrix,information entropy,distribution,maximum distribution,approximate and positive region,we construct the Hu＇s simplified discernibility matrix at first. Secondly,simplified discernibility matrix based on positive region is also constructed,and the corresponding attribute reduction definition is proposed. At the same time,it is proved that the attribute reduction definition of simplified discernibility matrix based on positive region is equal to that based on positive region. Thirdly,by using Hu＇s simplified discernibility matrix,it is proved that if B satisfies ↓AФ≠mij∈M→mij∩B≠Ф,where M is Hu＇ s discernibility matrix.then B must satisfy H （D｜B）= H （D｜C）. By exploiting simplified discernibility matrix based on positive region and simplified discernibility matrix based on approximate reduction,lt is also proved that if B is approximate consistent set,then B must satisfy POSB（D）= POSC（D）. According to the existed research results, the relationships of these six different definitions about attribute reduction are obtained.

关 键 词：粗糙集 HU差别矩阵 信息熵 分布约简 最大分布约简 近似约简 正区域 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]