摘要
考虑论域上一二元关系所决定的模糊粗糙近似算子的拓扑性质,证明了任一自反二元关系可以决定一模糊拓扑。并且,当二元关系自反对称时,该模糊拓扑中的元是开集当且仅当它是闭集;当二元关系自反传递时,该模糊拓扑的闭包与内部算子恰为模糊粗糙上、下近似算子。
In this paper we discusses the topological properties of fuzzy rough aqproximation operators generated by binary relation on the universe. It is proved that any reflexive binary relation determines a fuzzy topology. And, if the binary relation is a reflexive and symmetric, then the objects of this fuzzy topology is open if and only if closed; if the binary relation is a reflexive and transitive, then the closure and interior operators of this fuzzy topology is the fuzzy rough upper and lower approximations operators.
出处
《模糊系统与数学》
CSCD
北大核心
2008年第6期163-166,共4页
Fuzzy Systems and Mathematics
基金
国家自然科学基金资助项目(60474022)
关键词
近似空间
模糊粗糙集
模糊粗糙似算子
模糊拓扑
Approximation Space
Fuzzy Rough Set
Fuzzy Rough Approximations Operators
Fuzzy Topology
