一般关系下粗糙集上映射的拓扑性质

Topological Properties of Map on General Rough Sets

讨论了一般关系下粗糙集模型上映射的拓扑性质,指出一般关系下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一个二元关系,从而得到了两个粗集拓扑空间的映射。如果R是自反和传递的,则这个映射是连续的。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 rough sets model in general relation were discussed.The map between rough set model and the finite set can induce a binary relation on the finite set which led to a map on these two rough sets. If R is reflective and transitive, then the map is continuous.If the map is biejective, then it is simultaneously open and continuous, and both the image and inverse one of the rough set are rough.