| 粗糙近似算子的拓扑性质 |
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| 引用本文： | 秦克云,裴峥,杜卫锋.粗糙近似算子的拓扑性质[J].系统工程学报,2006,21(1):81-85. |
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| 作者姓名： | 秦克云 裴峥 杜卫锋 |
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| 作者单位： | 1. 西南交通大学数学系,四川,成都,610031
2. 西华大学计算机与数理学院,四川,成都,610039 |
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| 基金项目： | 国家自然科学基金资助项目(60474022) |
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| 摘 要： | 通过闭包与内部算子研究模糊粗糙集的拓扑结构,证明了自反、传递关系下的近似空间中模糊集的上、下近似算子分别为一个模糊拓扑的闭包、内部算子,且相应的模糊拓扑满足(TC)条件;反之,满足(TC)条件的模糊拓扑的闭包与内部算子也恰为一自反、传递关系下的近似空间中的上、下近似算子.
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| 关 键 词： | 粗糙集 模糊粗糙集 模糊拓扑 (TC)条件 |
| 文章编号： | 1000-5781（2006）01-0081-05 |
| 收稿时间： | 2003-08-12 |
| 修稿时间： | 2003-08-122003-11-24 |
Topological properties of rough approximation operators |
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| QIN Ke-yun,PEI Zheng,DU Wei-feng.Topological properties of rough approximation operators[J].Journal of Systems Engineering,2006,21(1):81-85. |
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| Authors: | QIN Ke-yun PEI Zheng DU Wei-feng |
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| Abstract: | Based on closure and interior operators this paper discusses the topological structure of fuzzy rough sets.In a approximation space which is based on a reflexive and transitive relation,it is proved that the upper and lower approximations of fuzzy sets are closure and interior operators of a fuzzy topology respectively and the fuzzy topology satisfy(TC) condition;Conversely,the closure and interior operators of a fuzzy topology which satisfy(TC) condition are exactly the upper and lower approximations of a approximation space respectively. |
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| Keywords: | rough set fuzzy rough set fuzzy topology (TC) condition |
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