| 自反、传递（模糊）关系与拓扑空间 |
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| 引用本文： | 郑顶伟,;蔡长勇.自反、传递（模糊）关系与拓扑空间[J].广西师院学报,2014(1):28-30. |
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| 作者姓名： | 郑顶伟 ;蔡长勇 |
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| 作者单位： | [1]华南理工大学数学系,广东广州510640; [2]广西大学数学与信息科学学院,广西南宁530004; [3]广西师范学院数学科学学院,广西南宁530023 |
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| 基金项目： | 广西自然科学基金（2013GXNSFBA019016）;广西大学科研资助项目（XJZ130362） |
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| 摘 要： | 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.
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| 关 键 词： | 模糊数学 自反 传递 拓扑空间 |
Reflexive,Transitive （Fuzzy） Relation and Topological Spaces |
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| Institution: | ZHENG Ding-wei , CAI Chang yong (1 .Department of Mathematics, South (hina University of Technology, Guangzhou 510640 2. College of Mathematics and Information Sciences, Guangxi University, Nanning 530004 3. School of Mathematical Sciences, Guangxi Teachers Education University, Nanning 530023 , (hina (hina China) |
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| Abstract: | 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. |
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| Keywords: | fuzzy mathematics reflexive zransizive zopological space |
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