Connectivity for matroids based on rough sets
  In mathematics and computer science, connectivity is one of the basic
concepts of matroid theory: it asks for the minimum number of elements which
need to be removed to disconnect the remaining nodes from each other. It is
closely related to the theory of network flow problems. The connectivity of a
matroid is an important measure of its robustness as a network. Therefore, it
is very necessary to investigate the conditions under which a matroid is
connected. In this paper, the connectivity for matroids is studied through
relation-based rough sets. First, a symmetric and transitive relation is
introduced from a general matroid and its properties are explored from the
viewpoint of matroids. Moreover, through the relation introduced by a general
matroid, an undirected graph is generalized. Specifically, the connection of
the graph can be investigated by the relation-based rough sets. Second, we
study the connectivity for matroids by means of relation-based rough sets and
some conditions under which a general matroid is connected are presented.
Finally, it is easy to prove that the connectivity for a general matroid with
some special properties and its induced undirected graph is equivalent. These
results show an important application of relation-based rough sets to matroids.
