Covering-Based Rough Sets on Eulerian Matroids
Rough set theory is an efficient and essential tool for dealing with vagueness and granularity in information systems. Covering-based rough set theory is proposed as a significant generalization of classical rough sets. Matroid theory is a vital structure with high applicability and borrows extensiv...
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Series: | Journal of Applied Mathematics |
Online Access: | http://dx.doi.org/10.1155/2013/254797 |
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doaj-92433ee74fa44b3194162cb267b933e72020-11-24T23:15:17ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/254797254797Covering-Based Rough Sets on Eulerian MatroidsBin Yang0Ziqiong Lin1William Zhu2Lab of Granular Computing, Minnan Normal University, Zhangzhou 363000, ChinaLab of Granular Computing, Minnan Normal University, Zhangzhou 363000, ChinaLab of Granular Computing, Minnan Normal University, Zhangzhou 363000, ChinaRough set theory is an efficient and essential tool for dealing with vagueness and granularity in information systems. Covering-based rough set theory is proposed as a significant generalization of classical rough sets. Matroid theory is a vital structure with high applicability and borrows extensively from linear algebra and graph theory. In this paper, one type of covering-based approximations is studied from the viewpoint of Eulerian matroids. First, we explore the circuits of an Eulerian matroid from the perspective of coverings. Second, this type of covering-based approximations is represented by the circuits of Eulerian matroids. Moreover, the conditions under which the covering-based upper approximation operator is the closure operator of a matroid are presented. Finally, a matroidal structure of covering-based rough sets is constructed. These results show many potential connections between covering-based rough sets and matroids.http://dx.doi.org/10.1155/2013/254797 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Bin Yang Ziqiong Lin William Zhu |
spellingShingle |
Bin Yang Ziqiong Lin William Zhu Covering-Based Rough Sets on Eulerian Matroids Journal of Applied Mathematics |
author_facet |
Bin Yang Ziqiong Lin William Zhu |
author_sort |
Bin Yang |
title |
Covering-Based Rough Sets on Eulerian Matroids |
title_short |
Covering-Based Rough Sets on Eulerian Matroids |
title_full |
Covering-Based Rough Sets on Eulerian Matroids |
title_fullStr |
Covering-Based Rough Sets on Eulerian Matroids |
title_full_unstemmed |
Covering-Based Rough Sets on Eulerian Matroids |
title_sort |
covering-based rough sets on eulerian matroids |
publisher |
Hindawi Limited |
series |
Journal of Applied Mathematics |
issn |
1110-757X 1687-0042 |
publishDate |
2013-01-01 |
description |
Rough set theory is an efficient and essential tool for dealing with vagueness and granularity in information systems. Covering-based rough set theory is proposed as a significant generalization of classical rough sets. Matroid theory is a vital structure with high applicability and borrows extensively from linear algebra and graph theory. In this paper, one type of covering-based approximations is studied from the viewpoint of Eulerian matroids. First, we explore the circuits of an Eulerian matroid from the perspective of coverings. Second, this type of covering-based approximations is represented by the circuits of Eulerian matroids. Moreover, the conditions under which the covering-based upper approximation operator is the closure operator of a matroid are presented. Finally, a matroidal structure of covering-based rough sets is constructed. These results show many potential connections between covering-based rough sets and matroids. |
url |
http://dx.doi.org/10.1155/2013/254797 |
work_keys_str_mv |
AT binyang coveringbasedroughsetsoneulerianmatroids AT ziqionglin coveringbasedroughsetsoneulerianmatroids AT williamzhu coveringbasedroughsetsoneulerianmatroids |
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1725591225091751936 |