邻域互补信息度量及其启发式属性约简  

Neighborhood Complementary Information Measures and Heuristic Attribute Re⁃duction

作　　者：陈帅 张贤勇 唐玲玉[1,2] 姚岳松 CHEN Shuai;ZHANG Xianyong;TANG Lingyu;YAO Yuesong(School of Mathematical Sciences,Sichuan Normal University,Chengdu,610066,China;Institute of Intelligent Information and Quantum Information,Sichuan Normal University,Chengdu,610066,China)

机构地区：[1]四川师范大学数学科学学院,成都610066 [2]四川师范大学智能信息与量子信息研究所,成都610066

出　　处：《数据采集与处理》2020年第4期630-641,共12页Journal of Data Acquisition and Processing

基　　金：国家自然科学基金(61673258)资助项目;四川省科技基金(19YYJC2845)资助项目;四川省青年科技基金(2017JQ0046)资助项目。

摘　　要：信息熵体系是进行不确定刻画与近似推理的重要理论,已经被引入粗糙集进行数据分析与智能处理。经典的互补熵、互补条件熵和互补互信息能够刻画粗糙性与模糊性,该信息体系的拓展具有应用意义。本文基于邻域粗糙集,扩张构建邻域互补信息度量并研究其启发式属性约简。通过解析式模拟与信息粒替换,定义邻域互补熵、邻域互补条件熵和邻域互补互信息,得到系统方程、双界刻画和粒化非单调性;基于邻域互补互信息,提出非单调属性约简并设计启发式约简算法;采用决策表实例与UCI数据实验有效验证性质与算法。基于邻域扩张,相关信息度量与属性约简具有应用前景。The information entropy system serves as a fundamental theory of uncertainty description and approximate reasoning,and it has been introduced into rough sets to implement data analyses and intelligence processing.Classical complementary entropy,conditional-entropy and mutual-information can effectively describe roughness and fuzziness,and their system expansion has application significance.In terms of neighborhood rough sets,neighborhood complementary information measures are extendedly constructed,and their heuristic attribute reduction is investigated.According to analytical simulation and granular replacement,neighborhood complementary entropy,conditional-entropy and mutual-information are defined,and their system equation,double bounds and granulation non-monotonicity are achieved.Based on the neighborhood complementary mutual-information,non-monotonic attribute reduction and its heuristic reduction algorithm are proposed.The validity of property and algorithm is verified by decision tables and data experiments.By virtue of neighborhood expansion,relevant information measures and attribute reduction have application prospects.

关 键 词：邻域粗糙集 信息论 邻域互补信息度量 不确定性 属性约简 粒计算 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]