区间值信息系统的熵度量  

Entropy Measurement for Interval-Valued Information Systems

作　　者：冯琴荣[1] 温玮华 FENG Qin-rong;WEN Wei-hua(School of Mathematics and Computer Science,Shanxi Normal University,Linfen Shanxi 041004)

机构地区：[1]山西师范大学数学与计算机科学学院,山西临汾041004

出　　处：《电子科技大学学报》2021年第1期101-105,共5页Journal of University of Electronic Science and Technology of China

基　　金：山西省自然科学基金(2016D011043)。

摘　　要：不确定性度量是粗糙集理论的一个主要研究问题,其中熵度量受到学者们的广泛关注。然而,迄今为止,区间值信息系统的香农熵度量研究较少,尤其缺乏满足单调性的香农熵度量。为此,该文首先给出了一种由覆盖导出划分的方法,并证明了覆盖越细,由其导出的划分越细,从而可用划分熵对区间值信息系统的不确定性进行度量;其次,分别构造了区间值信息系统的香农熵度量和补熵(粒度)度量,并证明了其单调性和有界性。最后,分析了香农熵和补熵的关系。Uncertainty measurement is one of the major research problems in rough set theory,and the entropy measure has caught many attentions.However,there is still less research about Shannon entropy measure with monotonicity for interval-valued information systems.For this purpose,firstly,this paper proposes a method of inducing a partition from a given covering and proves that the finer the covering,the finer the partition derived from it,so that partition entropy can be used to measure the uncertainty of interval-valued information system.Secondly,the Shannon entropy measure and the co-entropy(granularity)measure for interval-valued information systems are constructed respectively,and their monotonicity and boundedness are proved.At last,the relationship between Shannon entropy and co-entropy is analyzed.

关 键 词：补熵 区间值信息系统 香农熵 不确定性度量 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]