Dependence space of matroids and its application to attribute reduction
  Attribute reduction is a basic issue in knowledge representation and data
mining. Rough sets provide a theoretical foundation for the issue. Matroids
generalized from matrices have been widely used in many fields, particularly
greedy algorithm design, which plays an important role in attribute reduction.
Therefore, it is meaningful to combine matroids with rough sets to solve the
optimization problems. In this paper, we introduce an existing algebraic
structure called dependence space to study the reduction problem in terms of
matroids. First, a dependence space of matroids is constructed. Second, the
characterizations for the space such as consistent sets and reducts are studied
through matroids. Finally, we investigate matroids by the means of the space
and present two expressions for their bases. In a word, this paper provides new
approaches to study attribute reduction.
