The vectorially matroidal structure of generalized rough sets based on relations

This paper establishes the vectorially matroidal structure of generalized rough sets based on relations. Any relation induces the vectorial matroid through the representing matrix of the relation. And the neighborhood in generalized rough sets based on relations is connected with the circuit of the vectorial matroid. On the other hand, an approach to induce the relation by a matroid is provided. And the relationship between two inductions is studied. Results show that these two inductions are converse if and only if the relation is an equivalence one.