Relation matroid and its relationship with generalized rough set based
  on relation
  Recently, the relationship between matroids and generalized rough sets based
on relations has been studied from the viewpoint of linear independence of
matrices. In this paper, we reveal more relationships by the predecessor and
successor neighborhoods from relations. First, through these two neighborhoods,
we propose a pair of matroids, namely predecessor relation matroid and
successor relation matroid, respectively. Basic characteristics of this pair of
matroids, such as dependent sets, circuits, the rank function and the closure
operator, are described by the predecessor and successor neighborhoods from
relations. Second, we induce a relation from a matroid through the circuits of
the matroid. We prove that the induced relation is always an equivalence
relation. With these two inductions, a relation induces a relation matroid, and
the relation matroid induces an equivalence relation, then the connection
between the original relation and the induced equivalence relation is studied.
Moreover, the relationships between the upper approximation operator in
generalized rough sets and the closure operator in matroids are investigated.
