Matroidal Structure of Rough Sets from the Viewpoint of Graph Theory
Constructing structures with other mathematical theories is an important research field of rough sets. As one mathematical theory on sets, matroids possess a sophisticated structure. This paper builds a bridge between rough sets and matroids and establishes the matroidal structure of rough sets. In...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/973920 |
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| _version_ | 1850230225070194688 |
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| author | Jianguo Tang Kun She William Zhu |
| author_facet | Jianguo Tang Kun She William Zhu |
| author_sort | Jianguo Tang |
| collection | DOAJ |
| description | Constructing structures with other mathematical theories is an important research field of rough sets. As one mathematical theory on sets, matroids possess a sophisticated structure. This paper builds a bridge between rough sets and matroids and establishes the matroidal structure of rough sets. In order to understand intuitively the relationships between these two theories, we study this problem from the viewpoint of graph theory. Therefore, any partition of the universe can be represented by a family of complete graphs or cycles. Then two different kinds of matroids are constructed and some matroidal characteristics of them are discussed, respectively. The lower and the upper approximations are formulated with these matroidal characteristics. Some new properties, which have not been found in rough sets, are obtained. Furthermore, by defining the concept of lower approximation number, the rank function of some subset of the universe and the approximations of the subset are connected. Finally, the relationships between the two types of matroids are discussed, and the result shows that they are just dual matroids. |
| format | Article |
| id | doaj-art-210d02dda2e8426fa2be5db89d32874d |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-210d02dda2e8426fa2be5db89d32874d2025-08-20T02:03:57ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/973920973920Matroidal Structure of Rough Sets from the Viewpoint of Graph TheoryJianguo Tang0Kun She1William Zhu2School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, ChinaSchool of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, ChinaLab of Granular Computing, Zhangzhou Normal University, Zhangzhou 363000, ChinaConstructing structures with other mathematical theories is an important research field of rough sets. As one mathematical theory on sets, matroids possess a sophisticated structure. This paper builds a bridge between rough sets and matroids and establishes the matroidal structure of rough sets. In order to understand intuitively the relationships between these two theories, we study this problem from the viewpoint of graph theory. Therefore, any partition of the universe can be represented by a family of complete graphs or cycles. Then two different kinds of matroids are constructed and some matroidal characteristics of them are discussed, respectively. The lower and the upper approximations are formulated with these matroidal characteristics. Some new properties, which have not been found in rough sets, are obtained. Furthermore, by defining the concept of lower approximation number, the rank function of some subset of the universe and the approximations of the subset are connected. Finally, the relationships between the two types of matroids are discussed, and the result shows that they are just dual matroids.http://dx.doi.org/10.1155/2012/973920 |
| spellingShingle | Jianguo Tang Kun She William Zhu Matroidal Structure of Rough Sets from the Viewpoint of Graph Theory Journal of Applied Mathematics |
| title | Matroidal Structure of Rough Sets from the Viewpoint of Graph Theory |
| title_full | Matroidal Structure of Rough Sets from the Viewpoint of Graph Theory |
| title_fullStr | Matroidal Structure of Rough Sets from the Viewpoint of Graph Theory |
| title_full_unstemmed | Matroidal Structure of Rough Sets from the Viewpoint of Graph Theory |
| title_short | Matroidal Structure of Rough Sets from the Viewpoint of Graph Theory |
| title_sort | matroidal structure of rough sets from the viewpoint of graph theory |
| url | http://dx.doi.org/10.1155/2012/973920 |
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