Geometric Lattice Structure of Covering and Its Application to Attribute Reduction through Matroids
The reduction of covering decision systems is an important problem in data mining, and covering-based rough sets serve as an efficient technique to process the problem. Geometric lattices have been widely used in many fields, especially greedy algorithm design which plays an important role in the re...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/183621 |
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| _version_ | 1832552605670178816 |
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| author | Aiping Huang William Zhu |
| author_facet | Aiping Huang William Zhu |
| author_sort | Aiping Huang |
| collection | DOAJ |
| description | The reduction of covering decision systems is an important problem in data mining, and covering-based rough sets serve as an efficient technique to process the problem. Geometric lattices have been widely used in many fields, especially greedy algorithm design which plays an important role in the reduction problems. Therefore, it is meaningful to combine coverings with geometric lattices to solve the optimization problems. In this paper, we obtain geometric lattices from coverings through matroids and then apply them to the issue of attribute reduction. First, a geometric lattice structure of a covering is constructed through transversal matroids. Then its atoms are studied and used to describe the lattice. Second, considering that all the closed sets of a finite matroid form a geometric lattice, we propose a dependence space through matroids and study the attribute reduction issues of the space, which realizes the application of geometric lattices to attribute reduction. Furthermore, a special type of information system is taken as an example to illustrate the application. In a word, this work points out an interesting view, namely, geometric lattice, to study the attribute reduction issues of information systems. |
| format | Article |
| id | doaj-art-f386b593784c42f98a795bac1586e1d3 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-f386b593784c42f98a795bac1586e1d32025-02-03T05:58:16ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/183621183621Geometric Lattice Structure of Covering and Its Application to Attribute Reduction through MatroidsAiping Huang0William Zhu1Lab of Granular Computing, Minnan Normal University, Zhangzhou 363000, ChinaLab of Granular Computing, Minnan Normal University, Zhangzhou 363000, ChinaThe reduction of covering decision systems is an important problem in data mining, and covering-based rough sets serve as an efficient technique to process the problem. Geometric lattices have been widely used in many fields, especially greedy algorithm design which plays an important role in the reduction problems. Therefore, it is meaningful to combine coverings with geometric lattices to solve the optimization problems. In this paper, we obtain geometric lattices from coverings through matroids and then apply them to the issue of attribute reduction. First, a geometric lattice structure of a covering is constructed through transversal matroids. Then its atoms are studied and used to describe the lattice. Second, considering that all the closed sets of a finite matroid form a geometric lattice, we propose a dependence space through matroids and study the attribute reduction issues of the space, which realizes the application of geometric lattices to attribute reduction. Furthermore, a special type of information system is taken as an example to illustrate the application. In a word, this work points out an interesting view, namely, geometric lattice, to study the attribute reduction issues of information systems.http://dx.doi.org/10.1155/2014/183621 |
| spellingShingle | Aiping Huang William Zhu Geometric Lattice Structure of Covering and Its Application to Attribute Reduction through Matroids Journal of Applied Mathematics |
| title | Geometric Lattice Structure of Covering and Its Application to Attribute Reduction through Matroids |
| title_full | Geometric Lattice Structure of Covering and Its Application to Attribute Reduction through Matroids |
| title_fullStr | Geometric Lattice Structure of Covering and Its Application to Attribute Reduction through Matroids |
| title_full_unstemmed | Geometric Lattice Structure of Covering and Its Application to Attribute Reduction through Matroids |
| title_short | Geometric Lattice Structure of Covering and Its Application to Attribute Reduction through Matroids |
| title_sort | geometric lattice structure of covering and its application to attribute reduction through matroids |
| url | http://dx.doi.org/10.1155/2014/183621 |
| work_keys_str_mv | AT aipinghuang geometriclatticestructureofcoveringanditsapplicationtoattributereductionthroughmatroids AT williamzhu geometriclatticestructureofcoveringanditsapplicationtoattributereductionthroughmatroids |