粗糙集和拓扑空间

Rough Sets and the Topological Space

研究了粗糙集和拓扑空间的关系 ,讨论了Pawlak粗糙集模型的拓扑性质 ,指出Pawlak粗糙集模型等价于一类特殊的正则拓扑空间 ,该拓扑空间一般不是Hausdorff空间 ,且一般不具有连通性 .还证明了一个一般的二元关系下的粗糙集模型当且仅当它是自反的和传递的时 ,可定义一个拓扑空间 。

The relation between the rough sets and the topological space is studied. The topological properties of Pawlak rough sets model are discussed and that the Pawlak rough sets model is equivalent to a specical kind of regular topological space is pointed out. This topological space is generally not Hausdorff space and connectivity. It is also proven that a general rough set model can induce a topological space if and only if it is reflexive and transitive, and every topological space is a special approximation space.