基于邻域的覆盖粗糙集的上近似拟阵结构

Matroidal structure of the upper approximation of covering-based rough set defined by the neighborhood

通过邻域,构造了一个覆盖粗糙集的上近似拟阵结构。借助拟阵理论中的横贯理论和基公理,建立了这个拟阵。利用补邻域的下近似等价表示了一个与邻域相关的集族。最后从基数的角度研究了这个集族为这个拟阵的全体超平面的一个充要条件。

By neighborhoods,a matroidal structure of the upper approximation of covering-based rough sets is construc-ted.Through transversal theory and base axioms,the matroidal structure is established.By the lower approximations of the complementary neighborhood,a family related to neighborhoods is equivalent represented.Finally,a sufficient and necessary condition for the family to be the set of all hyperplanes of the matroid is studied from the viewpoint of cardi-nality.