摘要
本文研究了广义近似空间的拓扑性质。首先证明了论域上任意二元关系均能诱导一个Alexandrov拓扑,并讨论了该拓扑的若干性质。其次给出了论域上两个不同二元关系诱导同一个拓扑的充分必要条件。最后在全体二元关系之集上定义了一个等价关系,并研究了等价类的结构。
Topological properties of generalized approximation space arestudied in this paper. Firstly, it is proved that any binaryrelation on universe can induce an Alexandrov topology. Someproperties of this topology are discussed. Secondly, a sufficientand necessary condition of two different binary relations inducingthe same topology is presented. Finally, a equivalence relation isdefined on the set of all binary relations, and the structure of theequivalence class is studied.
出处
《模糊系统与数学》
CSCD
北大核心
2016年第5期174-178,共5页
Fuzzy Systems and Mathematics
基金
国家自然科学基金资助项目(61272015)
河南省高等学校重点科研项目(15A520087
16A520064)
校青年科学基金资助项目(2013-QNJJ-002)
关键词
粗糙集
拓扑
二元关系
预序
近似空间
rough set
topology
binary relation
preorder
approximation space
