粗糙集上映射的拓扑性质

Topological Properties of Map on Rough Sets

讨论了Pawlak粗糙集模型上映射的拓扑性质,指出Pawlak粗糙集模型与一个有限集之间的映射,可以诱导出在此有限集上的等价关系,从而得到了两个粗集拓扑空间的映射,这个映射是连续的。如果是双射,则此映射是开的且把粗集映成粗集,粗集的原像还是粗集。

Topological properties of map on Pawlak rough sets model are discussed.And a map between rough set model and a finite set can induce a equivalent relation on the finite set. If the map is regarded as a map between two topological spaces, then it is continuous. Furthermore, if the map is bijective, then it is simultaneously open and continuous,the image and the inverse image of a rough set are rough.