基于抽象相关关系的粗糙集研究 *

南京大学学报(自然科学版) ›› 2010, Vol. 46 ›› Issue (5): 507–510.

基于抽象相关关系的粗糙集研究 *

王石平 1 , 祝峰 2 ** , 朱培勇 1

出版日期:2015-04-02 发布日期:2015-04-02
作者简介: (1. 电子科技大学数学科学学院, 2. 计算机科学与工程学院, 成都, 611731)
基金资助:
国家自然科学基金( 60873077)

Abstract interdependency in rough sets

Wang Shi Ping 1 , William Zhu 2 , Zhu Pei Yong 1

Online:2015-04-02 Published:2015-04-02
About author: (1. School of Mathematical Sciences, 2. School of Computer Science and Engineering,
U niversity of Electronic Science and T echnology of China, Chengdu, 611731, China)

摘要/Abstract

摘要： 通过定义抽象相关关系这一概念来研究覆盖粗糙集. 借助群论中的思想, 在覆盖上进行抽象, 从而在覆盖粗糙集中定义了元素与元素的抽象相关关系, 元素与集合的依赖关系. 进而在粗糙集上定义
了独立集、基、秩函数等概念, 并在此基础上研究覆盖粗糙集的约简等性质. 把这些概念放在 Pawlak 粗糙集环境中进行讨论, 所得到的结果与 Pawlak 粗糙集理论中已有的结论相吻合, 如本文中用秩函数定
义的闭包算子等于 Pawlak 粗糙集中的上近似算子.

Abstract: Vagueness and incompleteness in information systems are important issues in data mining and information processing. Rough set theory is an efficient and effective tool to deal with these problems while
covering-based rough set theory is an extension to classical rough sets. In this paper, we investigate abstract interdependency in covering -based rough sets. Firstly, we propose several concepts such as base, rank function, and
independent set to describe abstract interdependency among elements of a covering in covering-based rough sets. Then we establish the relationships between these new concepts and other concepts already existing in covering
based rough sets such as reducible elements and approximation operators. Finally, we apply these concepts and results to classical rough sets. As a result, we get a conclusion that a closure operator defined with the rank function
we proposed is equal to the upper approximation operator.

王石平 1 , 祝峰 2 ** , 朱培勇 1 . 基于抽象相关关系的粗糙集研究 *

[J]. 南京大学学报(自然科学版), 2010, 46(5): 507–510.

Wang Shi Ping 1 , William Zhu 2 , Zhu Pei Yong 1 . Abstract interdependency in rough sets

[J]. Journal of Nanjing University(Natural Sciences), 2010, 46(5): 507–510.

参考文献

[ 1 ] Zhu W. Generalized rough sets based on rela tions. Information Science, 2007, 177 ( 22) : 4997~ 5011.
[ 2 ] Zhu W. Relationship between generalized rough sets based on binary relation and covering. Information Science, 2009, 179( 3) : 210~ 225.
[ 3 ] Yao Y Y. Relational interpretations of neighborhood operators and rough set approximation operators. Information Sciences, 1998, 101 (1- 4) : 239~ 259.
[ 4 ] Zhu W, Wang F Y. Reduction and axiomization of covering generalized rough sets. Information Sciences, 2003, 152( 1) : 217~ 230.
[ 5 ] Zhu W, Wang F Y. On three types of covering rough sets. IEEE Transactions on Knowledge and Data Engineering, 2007, 19 ( 8 ): 1131~ 1144.
[ 6 ] Zhu W. Relationship among basic concepts in covering-based rough sets. Information Sciences, 2009, 17( 14): 2478~ 2486.
[ 7 ] Andrzej S. On topology in information system. Bulletin of Polish Academic Science and Mathematics, 1988, 36: 477~ 480.
[ 8 ] Zhu W. Topological approaches to covering rough sets. Information Sciences, 2007, 177(6) : 1499~ 1508.
[ 9 ] Liu G L, Zhu W. T he algebraic structures of generalized rough set theory. Information Sciences, 2008, 178(21) : 4105~ 4113.
[ 10] Zdzislaw P, Andrzej S. Rough sets and boolean reasoning. Information Science, 2007, 177( 1): 41~ 73.
[ 11] Zdzislaw P. Rough sets: Theoretical aspects of reasoning about data. Boston: Kluwer Academic Publishers, 1991, 1~ 237.
[ 12] Lai H J. Matroid theory. Beijing: Higher Education Press, 2002, 6~ 24. ( 赖虹建. 拟阵论. 北京: 高等教育出版社, 2002, 6~ 24).
[ 13] Hu J, Wang G Y. Hierarchical model of covering granular space. Journal of Nanjing Universuty( Natural Sciences) , 2008, 44( 5): 551~ 558. (胡? 军, 王国胤. 覆盖粒度空间的层次模型. 南京大学学报( 自然科学), 2008, 44( 5): 551~ 558).

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