Rough Approximation Operators on Matroids Via Circuits

In this paper, we investigate a pair of rough approximation operators on matroids through circuits. Firstly, an equivalence relation is induced by circuits of a matroid, and some representations of the pair of approximation operators with respect to the equivalence relation are presented. These representations are presented from a family of circuits and a graph induced by circuits, respectively. Secondly, we illustrate that the pair of approximation operators are not the existing operators in matroids. Moreover, we investigate some characteristics of this pair of rough approximation operators on matroids. These characteristics are presented mainly through circuits and some operations in matroids. In a word, these results show an interesting view to investigate the combination between rough sets and matroids.