邻域粗糙集中不确定性的熵度量方法  

Uncertainty Measures Using Entropy and Neighborhood Rough Sets

作　　者：陈玉明[1,2] 曾志强[1] 田翠华[1] CHEN Yuming;ZENG Zhiqiang;TIAN Cuihua(College of Computer and Information Engineering, Xiamen University of Technology, Xiamen, Fujian 361024, China;State International S&T Cooperation Base of Networked Supporting Software, Jiangxi Normal University, Nanchang 330027, China)

机构地区：[1]厦门理工学院计算机与信息工程学院,福建厦门361024 [2]江西师范大学国家网络化支撑软件国际科技合作基地,南昌330027

出　　处：《计算机科学与探索》2016年第12期1793-1800,共8页Journal of Frontiers of Computer Science and Technology

基　　金：国家自然科学基金No.61573297;福建省自然科学基金Nos.2015J01277;2016J01324;福建省教育厅项目Nos.JA09217;JB13152;福建省高校新世纪优秀人才支持计划~~

摘　　要：针对传统粗糙集理论中不确定度量方法难以适用于邻域粗糙集模型的问题,引入信息熵的度量方法,提出了基于信息熵的邻域粗糙集不确定性度量方法。该方法采用邻域关系对连续型数据进行信息粒化,基于粒化后的数据定义邻域系统中的近似精度、邻域信息熵、加权邻域信息熵等不确定性度量。进一步提出邻域系统不确定性度量的公理化表示,证明邻域系统的近似精度、邻域信息熵、加权邻域信息熵都是公理化度量;给出其最大最小值,证明其满足单调性原理。理论分析与实验表明邻域系统中的信息熵度量优于近似精度度量。In view of the fact that the uncertainty measures of classical rough set theory are difficult to be suitable for neighborhood rough set model, this paper proposes an uncertainty measurement method based on information entropy and neighborhood rough sets. By the definitions of neighborhood relation, each object in the universe is assigned with a neighborhood subset, called neighborhood granule. Some uncertainty measures of neighborhood granule are defined, including approximate accuracy, information entropy and weighted information entropy in the neighborhood system. Furthermore, this paper presents the axiomatic concept of measure, and proves that the three measures are axiomatic uncertainty measures. This paper also gives the maximum and minimum of these measures and proves their monotonicities. Theoretical analysis and experiments show that the information entropy measure in the neighborhood system is better than the approximate accuracy measure.

关 键 词：邻域粗糙集 邻域信息熵 不确定性度量 信息系统 近似精度 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]