﻿粗糙集模型的拓广<br>The Extension of the Rough Set Model

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Computer Science and Application
Vol.3 No.4(2013), Article ID:12107,3 pages DOI:10.12677/CSA.2013.34039

The Extension of the Rough Set Model*

Mengjie Wang1, Aiqin Xu1, Yongjian Liu2, Weihua Wang1

1Department of Science, Wuhan University of Technology, Wuhan

2Department of Computer Science, Wuhan University of Technology, Wuhan

Email: 578067715@qq.com

Received: Apr. 28th, 2013; revised: May 16th, 2013; accepted: May 28th, 2013

Copyright © 2013 Mengjie Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ABSTRACT：

Because of the incomplete information and inequivalent binary relation on the domain, the classic rough set model will need to be expanded. On the one hand, the equivalence relations of the rough set model is extended to tolerance relations or inclusion relations, which can extend the application range. This paper studies high and low approximation operators on the basis of this method and compares with the two kinds of relations through case analysis. On the other hand, on the basic of granularity of knowledge structure and knowledge representation method, it studies the approximation operators from two aspects of neighborhood system and granularity.

Keywords: The Rough Set Model; Tolerance Relations; Contains Relations; Approximation Operators; Neighborhood Systems

1武汉理工大学理学院，武汉

2武汉理工大学计算机学院，武汉

Email: 578067715@qq.com

1. 引言

2. Pawlak的粗糙集模型

3. 等价关系的泛化

3.1. 容差关系

3.2. 包含关系

3.3. 案例分析

Table 1. An incomplete information table

4. 基本知识粒度的构造和知识的表示方法 的拓广

4.1. 基于粒度的上、下近似算子

4.2. 基于邻域系统的上、下近似算子

4.2.1. 邻域系统

1)为一族论域的集合；

2)个论域上的笛卡尔积，其中

3)称为一个元关系；

4)是一族等价关系的合集；称二元组为关系粒计算模型。

1)称为的邻域；

2)的所有邻域的合集称为的领域系统，记为，即

3) 集合称为的邻域系统，记为

4.2.2. 近似算子

1)

2)

3)

4.2.3. 案例分析

5. 结论

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[4]       马周明, 李进金. 基于强对称关系的广义粗糙集模型[J]. 模式识别与人工智能, 2012, 25(4): 558-563.

[5]       代春艳. 粗糙集理论及其应用发展综述[J]. 重庆工商大学学报, 2004, 21(6): 575-579.

[6]       杨习贝, 杨静宇. 邻域系统粗糙集模型[J]. 南京理工大学学报, 2012, 36(2): 292-293.

[7]       Y. H. Qian, J. Y. Liang and W. Wei. Pessimistic rough decision. Second International Workshop on Rough Sets Theory. Zhoushan, 19-21 October 2010, 440-449.

[8]       R. Slowinskn, D. Vanderpooten. A generalized definition of rough approximations. ICS Research Report, 1996.

NOTES

*资助项目：科技部“十二五”国家科技支撑计划课题“文化遗产知识本体构建存储可视化技术研究”(2012BAH33F03)。