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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 183621, 8 pages
http://dx.doi.org/10.1155/2014/183621
Research Article

Geometric Lattice Structure of Covering and Its Application to Attribute Reduction through Matroids

Lab of Granular Computing, Minnan Normal University, Zhangzhou 363000, China

Received 22 May 2013; Accepted 31 December 2013; Published 11 February 2014

Academic Editor: Jin L. Kuang

Copyright © 2014 Aiping Huang and William Zhu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.