Rough sets and partition matroids

In this paper rough sets are studied from the viewpoint of partition matroids. A partition matroid is expressed as the direct sum of some uniform matroids on the equivalence classes. We also study under what condition partition and partition matroid are determined by each other. Furthermore, it is interesting that the boundary region of a subset is obtained directly through the circuits of a partition matroid. And we represent the approximations of any subset of a universe by these circuits. Finally, the relationships between the approximation operators and the closure operators of partition matroids are established. These results enrich rough set theory and matroid theory.