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2014 Geometric Lattice Structure of Covering and Its Application to Attribute Reduction through Matroids
Aiping Huang, William Zhu
J. Appl. Math. 2014: 1-8 (2014). DOI: 10.1155/2014/183621


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.


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Aiping Huang. William Zhu. "Geometric Lattice Structure of Covering and Its Application to Attribute Reduction through Matroids." J. Appl. Math. 2014 1 - 8, 2014.


Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07010563
MathSciNet: MR3170440
Digital Object Identifier: 10.1155/2014/183621

Rights: Copyright © 2014 Hindawi


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