Rough matroid

This paper proposes a framework to integrate rough sets with matroids. Specifically, we propose the lower and upper rough matroids which extend the matroid. They are established by the lower and upper approximations of generalized rough sets based on relations, respectively. As a generalization of the lower (upper) rough matroid, the lower (upper) rough greedoid is defined, and it also a generalization of the greedoid. Moreover, an axiom of poset matroid is provided by generalized rough sets based on relations. Finally, we prove that the poset matroid is a special case of the lower rough greedoid.