| Covering-based rough sets, as a technique of granular computing, can be a useful tool for dealing with inexact, uncertain or vague knowledge in information systems. Matroids generalize linear independence in vector spaces, graph theory and provide well established platforms for greedy algorithm design. In this paper, we construct three types of matroidal structures of covering-based rough sets. Moreover, through these three types of matroids, we study the relationships among these matroids induced by six types of covering-based upper approximation operators. First, we construct three families of sets by indiscernible neighborhoods, neighborhoods and close friends, respectively. Moreover, we prove that they satisfy independent set axioms of matroids. In this way, three types of matroidal structures of covering-based rough sets are constructed. Secondly, we study some characteristics of the three types of matroid, such as dependent sets, circuits, rank function and closure. Finally, by comparing independent sets, we study relationships among these matroids induced by six types of covering-based upper approximation operators. |
