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

[摘要] 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 algorithmdesign which plays an important role in the reduction problems. Therefore, it is meaningfulto combine coverings with geometric lattices to solve the optimization problems. In this paper, we obtain geometric lattices from coverings through matroids and thenapply them to the issue of attribute reduction. First, a geometric lattice structure of acovering is constructed through transversal matroids. Then its atoms are studied andused to describe the lattice. Second, considering that all the closed sets of a finite matroidform a geometric lattice, we propose a dependence space through matroids andstudy the attribute reduction issues of the space, which realizes the application of geometriclattices to attribute reduction. Furthermore, a special type of information systemis taken as an example to illustrate the application. In a word, this work points out aninteresting view, namely, geometric lattice, to study the attribute reduction issues ofinformation systems.

[学科分类] 应用数学