基于全相容性粒度的粗糙集模型

Rough set model based on the granulated view of complete compatibility

基于不完备信息系统下的容错关系粗糙集模型与完备信息系统下的粗糙集模型相比更能满足现实生活的需要,因此在实际工作中得到了广泛的应用,但其中存在的一个问题,即容错类中的元素并非两两存在相容关系,而只是都与其容错类的生成元素存在相容关系.本文首先重新定义了不完备信息系统下的相容关系,进而提出了最大全相容类的概念,从而保证了相容模块中的元素两两相容.在此基础上,定义了4种不同的知识表达系统,不仅对这4种不同的知识表达系统所构成的覆盖进行了比较,而且在不同的知识表达系统下对于粗糙集的近似精度,知识的粗糙熵以及粗糙集的粗糙熵进行了深入分析.

Rough set model based on tolerance relation in incomplete information system has got broader applications in practice than the rough set model in complete information system because it further meets the needs of real life. However, one of the crucial problems of tolerance relation is that not all of the elements in a tolerance class have a mutual tolerance relation but they are all tolerant with the generating element of the tolerance class. In this paper, the compatible relation based on the incomplete information system is re-defined and then the maximal complete compatible class is proposed for the purpose that any two of the elements in the same compatible module are mutually compatible. Fullhermore, three different knowledge representation systems are defined and different coverings based on different knowledge representation systems are compared. Finally, for every knowledge representation system, the accuracy measure of rough set approxiwation, rough entropy of knowledge as well as rough entropy of rough set are deeply analyzed.