双论域粗糙集的不确定性度量

上海交通大学学报（自然版） ›› 2011, Vol. 45 ›› Issue (12): 1841-1845.

双论域粗糙集的不确定性度量

阎瑞霞，郑建国，翟育明

（东华大学旭日工商管理学院，上海 200051）

收稿日期:2011-10-26 出版日期:2011-12-31 发布日期:2011-12-31
基金资助:
国家自然科学基金资助项目(70971020)，上海市软科学博士学位论文项目(11692191400)

Uncertainty Measures of Rough Set over Dual-universes

YAN Rui-Xia, ZHENG Jian-Guo, DI Yu-Ming

(Glorious Sun School of Business Administration, Donghua University, Shanghai 200051, China)

Received:2011-10-26 Online:2011-12-31 Published:2011-12-31

摘要/Abstract

摘要： 为了进一步扩展粗糙集的应用范围和灵活性，利用构造性方法研究了双论域粗糙集的不确定性度量，分析了双论域粗糙集不确定性度量与由双论域粗糙集诱导的Pawlak粗糙集的粒度之间的关系.通过比较Pawlak近似空间中粒度的大小，定义了不同信息系统中关系的粗细程度，给出了反映信息系统分类能力的双论域粗糙集信息熵和信息粒度的定义，研究了双论域粗糙集信息熵和信息粒度与信息系统中关系的粗细程度之间的关系.结果表明：双论域粗糙集的信息熵越大，信息系统的不确定性越强，信息系统中关系的区分能力越弱；信息系统的关系越精细，双论域粗糙集的信息熵越小，双论域粗糙集的信息粒度越小.

关键词: 粗糙集, 双论域粗糙集, 信息熵, 信息粒度

Abstract: To broaden the application field of rough set, constructive method was utilized to research uncertainty measures of rough set over dual-universes. The relation between uncertainty measures of rough set over dualuniverses and Pawlak rough set induced by rough set over dual-universes was analyzed. The precision of relation in information system was discussed by comparing granular in Pawlak rough set. Information entropy and information granular of rough set over dual-universes were introduced to denote the classified ability in information systems. The relation between information entropy of rough set over dual-universes and the precision of relation in information system was studied. Also, the relation between information granular of rough set over dual-universes and the precision of relation in information system was researched. The results show that the bigger the information entropy, the stronger the uncertainty in information system is and the weaker the ability in information system is. The finer the relation in information system, the smaller the information entropy is and the smaller the information granular is.

Key words: rough set, rough set over dualuniverses, information entropy, information granular

中图分类号:

O159

阎瑞霞, 郑建国, 翟育明. 双论域粗糙集的不确定性度量[J]. 上海交通大学学报（自然版）, 2011, 45(12): 1841-1845.

YAN Rui-Xia, ZHENG Jian-Guo, DI Yu-Ming. Uncertainty Measures of Rough Set over Dual-universes[J]. Journal of Shanghai Jiaotong University, 2011, 45(12): 1841-1845.

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