一种基于粗糙集理论的互补信息熵的新定义  

A New Definition of Complementary Information Entropy Based on Rough Set Theory

作　　者：黄卫华[1] 

机构地区：[1]文山学院数学学院,云南文山663000

出　　处：《延安大学学报（自然科学版）》2016年第2期97-99,共3页Journal of Yan'an University：Natural Science Edition

基　　金：国家自然科学基金项目(11361074);云南省教育厅科研基金项目(2015Y470);文山学院重点学科数学建设项目(12WSXK01)

摘　　要：在粗糙集理论中给出了一种互补信息熵的新定义,该信息熵具有与香农熵相同的性质,即随着划分粒度的加细,互补信息熵单调增加。当划分为最大粒度时,信息熵取值为0;当划分为最小粒度时,信息熵取值为1-1/|U|。实例表明随着信息熵的增加,划分不一定变细,即定理3的逆命题一般情况下不成立。A new definition of complementary information entropy was given in rough set theory. The information entropy has the same nature as shannon entropy,i. e. the information entropy increases monotonically as the granula-rity of information becomes smaller through finer partitions. When divided into the largest particle size,the information entropy value is 0,When divided into a minimum size,the information entropy values is 1- 1 / ｜ U ｜. The example shows that the granularity of information not always becomes smaller through finer partitions monotonically as the information entropy increases,i. e. reverse relation of proposition 3 cannot be established in general.

关 键 词：近似空间 不确定性度量 互补信息熵 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]