| 覆盖下近似算子的拓扑性质 |
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| 引用本文： | 于海,张瑞玲,詹婉荣. 覆盖下近似算子的拓扑性质[J]. 模糊系统与数学, 2012, 26(3): 169-174 |
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| 作者姓名： | 于海 张瑞玲 詹婉荣 |
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| 作者单位： | 1. 洛阳师范学院数学科学学院,河南洛阳,471022
2. 洛阳师范学院信息技术学院,河南洛阳,471022 |
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| 基金项目： | 国家自然科学基金资助项目，河南省教育厅自然科学研究项目，洛阳师范学院青年科学基金资助项目 |
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| 摘 要： | 在不限制U为有限论域的情况下,研究了覆盖下近似算子XL和CL的拓扑性质。证明了覆盖下近似算子XL是内部算子,而且由XL生成的拓扑TXL为包含由覆盖C本身作为子基生成的拓扑TC的最小Alexandrov拓扑。特别地,当U为有限论域时,TXL=TC.然而,覆盖下近似算子CL不是内部算子。当覆盖C为某拓扑的基时,CL是内部算子,且此时由CL生成的拓扑TCL与TC是同一个拓扑。若进一步要求U为有限论域,则TCL=TXL=TC,进而CL=XL.
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| 关 键 词： | 覆盖近似空间 覆盖 下近似算子 拓扑 内部算子 |
The Topological Properties of Covering Lower Approximation Operators |
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| YU Hai , ZHANG Rui-ling , ZHAN Wan-rong. The Topological Properties of Covering Lower Approximation Operators[J]. Fuzzy Systems and Mathematics, 2012, 26(3): 169-174 |
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| Authors: | YU Hai ZHANG Rui-ling ZHAN Wan-rong |
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| Affiliation: | 1(1.Academy of Mathematics and Science,Luoyang Normal College,Luoyang 4710222,China;2.Academy of Information Technology,Luoyang Normal College,Luoyang 471022,China) |
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| Abstract: | The topological properties of covering lower approximation operators XL and CL are studied when the universe U is not restricted to be finite.It is proved that the covering lower approximation operator XL is an interior operator.Moreover the topology TXL generated by XL is the minimal Alexandrov topology including the topology TC whose subbase is the covering C.Particularly,when U is a finite universe,TXL=TC.However,the covering lower approximation operator CL is not an interior operator.When the covering C is a base of some topology,CL is an interior operator and TCL=TC,where TCL is the topology generated by CL.In this case,if U is a finite universe,then TCL=TXL=TC and CL=XL. |
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| Keywords: | Covering Approximation Space Covering Lower Approximation Operator Topology Interior Operator |
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