Relationship between covering-based rough sets and free matroids

被引：0

作者：

Yu, Chengyi ^{[1
,2
]}

Min, Fan ^{[1
]}

Zhu, William ^{[1
]}

机构：

[1] Lab of Granular Computing, Zhangzhou Normal University

[2] Department of Mathematics and Information Science, Zhangzhou Normal University

来源：

Advances in Information Sciences and Service Sciences | 2012年 / 4卷 / 12期

关键词：

Free matroid; Matroid; Reducible element; Reducible matroid; Rough set;

D O I：

10.4156/AISS.vol4.issue12.22

中图分类号：

学科分类号：

摘要：

Matroid was defined as a generalization of graph and matrix to try to capture abstractly essence of independence. It has been widely applied to computer science, mechanical engineering, and so on. Free matriod is an important matroid, it has some good characters. Covering-based rough set is a generalization of classical rough set in that the data model is covering rather than partition. In this paper, we study the relationships between covering-based rough sets and free matroids. Firstly, we establish the free matroidal structure of covering-based rough sets. On the one hand, any covering of a universe can be characterized by a family of free matroids. On the other hand, a family of free matroids can generate a covering. Furthermore, we study some basic properties of free matroidal structure of covering-based rough sets, such as rank function, base, and closure operator. Secondly, we investigate the relationships between reducible elements of a covering and reducible matroids in a family of free matroids induced by the covering. Reducible elements of a covering are redundant elements in covering-based rough sets, and reducible matroids are redundant matroids in a family of matroids. Actually, they are equivalent. A covering block in a covering is reducible if and only if the matroid induced by the covering block is a reducible matroid. These results enrich covering-based rough set theory and matroid theory.

引用

页码：193 / 200

页数：7

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