Relationship between the second type of covering-based rough set and
  matroid via closure operator
  Recently, in order to broad the application and theoretical areas of rough
sets and matroids, some authors have combined them from many different
viewpoints, such as circuits, rank function, spanning sets and so on. In this
paper, we connect the second type of covering-based rough sets and matroids
from the view of closure operators. On one hand, we establish a closure system
through the fixed point family of the second type of covering lower
approximation operator, and then construct a closure operator. For a covering
of a universe, the closure operator is a closure one of a matroid if and only
if the reduct of the covering is a partition of the universe. On the other
hand, we investigate the sufficient and necessary condition that the second
type of covering upper approximation operation is a closure one of a matroid.
