基于广义粗集覆盖约简的粗糙熵

在广义粗集覆盖约简理论中,由于集合的上下近似是由其覆盖约简来确定的,因此有必要寻求一种新的度量来刻画知识和粗集的粗糙性.通过引入信息熵以刻画广义粗集覆盖约简的知识粗糙性以及粗集粗糙性,提出了一种新的知识粗糙性和粗集粗糙性度量.得到知识粗糙熵和粗糙集的粗糙熵都随广义覆盖约简的变细而单调减少的结论,从信息论观点出发,对不完备信息系统粗集理论进行了探讨.

Rough Entropy Based on Generalized Rough Sets Covering Reduction

In generalized rough set covering reduction theory,it is necessary to find a new measure to knowledge and rough set because the upper and lower approximations of rough sets are determined by their covering reduction.In this paper,information entropy is introduced to discuss the rough entropy of knowledge and the roughness of rough set,based on generalized rough set covering reduction.A new kind of measurement about the roughness of knowledge and rough set is presented.The conclusion that the rough entropy of knowledge and rough set decreases monotonously as the generalized rough set covering reduction becomes finer is obtained.This paper presents some useful exploration about the incomplete information system from information views.