关键词: 粗糙集, 覆盖, 邻域, 近似算子, 拟阵

Abstract: In the topology theory, set-valued mapping is an important concept. According to the relationship of elements, a new type of matroidal structure is obtained due to set-valued mappings. Under this structure, some characteristics of this kind of matroid are investigated, such as independent sets, dependent sets, circuits, rank functions, closures and closed sets. At the same time, some equivalent characteristics of dual matroid with respect to this type of matroid are proposed, such as independent sets and circuits. In addition, based on the concept of neighborhood and approximation operator under the covering, the relationship between matroidal structure induced by set-valued mapping and rough set is established.

Key words: rough sets, covering, neighborhood, approximation, matroid