Connectedness of Graph and Matroid by Covering-Based Rough Sets

Abstract

Covering-based rough sets provide an efficient theory to process information in data mining. Matroid theory is a generalization of both linear algebra and graph theory, and has a variety of applications in many fields, such as covering-based rough sets. In this paper, we study the connectedness of graphs and matroids through covering-based rough sets. First, we present an approach to induce a covering by a graph. Then we use the covering upper approximation operator and the rank of matrix representation of the covering to study the connectedness of the graph. Moreover, we give the expression of the number of the connected components of a graph. Second, we establish a matroid based on the covering induced by a graph and study the connectedness of this matroid.