自反、传递(模糊)关系与拓扑空间

Reflexive,Transitive (Fuzzy) Relation and Topological Spaces

研究了自反传递模糊关系与拓扑空间的联系,证明了一个自反传递的模糊关系对应一个单调的拓扑空间族,从而对应一个模糊化拓扑.特别地,当R是自反传递关系时,该拓扑族退化为一个拓扑空间,该拓扑空间以粗糙下近似为其内部算子.

The relation between the reflexive , transitive fuzzy binary relation R with topological space is studied. We prove that a reflexive , transitive fuzzy binary relation has a corresponding to a fuzzying topology which is a monotone topological space, whence R is a reflexive , transitive relation, the fuzzying topology beconle a classical topology in which the closure and the interior operator is just the rough upper and lower approximation operator.