Matroidal structure of generalized rough sets based on symmetric and
  transitive relations
  Rough sets are efficient for data pre-process in data mining. Lower and upper
approximations are two core concepts of rough sets. This paper studies
generalized rough sets based on symmetric and transitive relations from the
operator-oriented view by matroidal approaches. We firstly construct a
matroidal structure of generalized rough sets based on symmetric and transitive
relations, and provide an approach to study the matroid induced by a symmetric
and transitive relation. Secondly, this paper establishes a close relationship
between matroids and generalized rough sets. Approximation quality and
roughness of generalized rough sets can be computed by the circuit of matroid
theory. At last, a symmetric and transitive relation can be constructed by a
matroid with some special properties.
