Relationship Between Covering Rough Sets Models And Matroidal Structure

Rough set theory is a useful mathematical tool for dealing with the incompleteness data and uncertainty data, it has wide application in artificial intelligence and data mining, etc. It possesses important theory significance and practical value to combine rough set with other theories. As a new research field, matroid theory is the abstraction and extension of graph theory and algebra concept, it has wide application in combinatorial optimization, integer programming, network flow and grid theory. In this paper, we combine the rough set with matroid. The main content of the paper is stated as follows:1. The covering approximation space is constructed by a family of subsets of the universe, which usually is not a covering. Then the relationship between covering approximation space and the transversal matroid induced by this family of subsets is discussed. In particular, the thesis present the sufficient condition under which a subset is a partial transversal, and also the necessary condition, and construct some types of circuits in the transversal matroid. Moreover, the thesis investigate the relationship between upper approximation operators based in the covering induced by a family of subsets and closure operators in transversal matroids. Finally. the thesis build two types of axiomatic characterizations of the covering approximation operator, based on set theory and matroid theory, respectively.2. From the viewpoint of rank function of matroid. we constructed a rank function in two types of generalized rough sets respectively, which are neighborhood-based rough set model and covering-based rough set model, then can obtain two matroidal structures. Moreover, we studied the relationship between this two matroidal structure and the two generalized rough sets models.