Characteristics of 2-circuit matroids through rough sets

Matroids generalize the linear independence in vector spaces, and they have many applications in diverse fields, especially in greedy algorithms. In this paper, 2-circuit matroids are defined and their several axioms are obtained through rough sets. First, we induce a matroid from a symmetric and transitive relation, and characterize it through generalized rough sets. Second, inspired by those characteristics of the matroid, we define 2-circuit matroids. Then several concise axioms of 2-circuit matroids are obtained using rough sets.