对称传递关系的诱导拓扑及其可数性
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摘要
粗糙集通过二元关系密切联系拓扑,并具有基于自反、自反传递、自反对称等关系的拓扑研究。采用对称传递关系构建拓扑并研究其可数性。基于对称传递关系,定义粗糙集近似集,由此建立拓扑及内部、闭包;针对构建拓扑,确立基与邻域基,得到第二可数性、第一可数性、可分性、林德洛夫性等可数性特征;提供实例分析。研究结果基于新二元关系揭示粗糙集与拓扑深入联系。
Rough sets depend on binary relations to closely adhere to topologies, and exhibit topology studies based on reflexive, reflexive and transitive, reflexive and symmetric relations. Thus, a symmetric and transitive relation is adopted to construct a topology, and its topological countability is investigated. Based on a symmetric and transitive relation,approximations of rough sets are defined, and the corresponding topology, interior and closure are constructed; according to the induced topology, the base and neighborhood base are established to gain countability including the second coutability and first coutability, separability, and Lindelof feature; example analyses are finally provided. The obtained results resort to the new type of binary relations to reveal in-depth connections between rough sets and topologies.
Rough sets depend on binary relations to closely adhere to topologies, and exhibit topology studies based on reflexive, reflexive and transitive, reflexive and symmetric relations. Thus, a symmetric and transitive relation is adopted to construct a topology, and its topological countability is investigated. Based on a symmetric and transitive relation,approximations of rough sets are defined, and the corresponding topology, interior and closure are constructed; according to the induced topology, the base and neighborhood base are established to gain countability including the second coutability and first coutability, separability, and Lindelof feature; example analyses are finally provided. The obtained results resort to the new type of binary relations to reveal in-depth connections between rough sets and topologies.
引文
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[2]唐小娟,丁树良.粗糙集理论在认知诊断中的应用[J].心理科学,2016(4):790-795.
[3]王国虎,薛进学.基于粗糙集理论与支持向量机的多传感器信息融合方法[J].现代制造工程,2016(5):59-62.
[4]王永生.基于粗糙集理论的动态数据挖掘关键技术研究[D].北京:北京科技大学,2016.
[5]葛浩.基于粗糙集的不协调决策系统知识约简研究[D].合肥:安徽大学,2016.
[6]叶回春,张世文,黄远仿.粗糙集理论在土壤肥力评价指标权重确定中的应用[J].中国农业科技,2014,47(4):710-717.
[7]刘慧玲.基于粗糙集理论的齿轮箱故障诊断研究[D].太原:中北大学,2013.
[8]曹洪洋,任晓莹.基于粗糙集理论的区域降雨型滑坡预测预报[J].水文地质工程地质,2017(2).
[9]桑秀丽,李哲,肖汉杰.肿瘤病理类型绿色诊断方法研究——基于变精度粗糙集与贝叶斯网络[J].统计与信息论坛,2015(4):71-77.
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[12]马周明,李进金.严格局部自反关系下的广义粗糙集[J].计算机工程与应用,2011,47(29):154-157.
[13]张宇.基于一般二元关系的几种粗糙集模型[D].辽宁锦州:渤海大学,2013.
[14]Pawlak Z.Rough sets:Theoretical aspects of reasoning about data[M].Boston:Kluwer Academic Publishers,1991.
[15]李招文,张珂.广义近似空间的拓扑结构[J].应用数学学报,2010,33(4):750-757.
[16]乔全喜.粗糙集的拓扑结构研究[D].成都:西南交通大学,2013.
[17]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.
[18]郑顶伟,蔡长勇.自反、传递(模糊)关系与拓扑空间[J].广西师范学院学报:自然科学版,2014,31(1):28-30.
[19]Yao Yiyu.Two views of the theory of rough sets in finite universes[J].International Journal of Approximate Reasoning,1996,15(4):291-317.
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[21]Qin Keyun.Generalized rough sets based on reflexive and transitive relations[J].Information Sciences,2008,178:4138-4141.
[22]Zhang Huapeng,Yao Ouyang,Wang Zhudeng.Note on“Generalized rough sets based on reflexive and transitive relations”[J].Information Sciences,2009,179(4):471-473.
[23]秦克云,裴峥,杜卫峰.粗糙近似算子的拓扑性质[J].系统工程学报,2006,21(1):81-85.
[24]吴志远.拓扑学在粗糙集理论中的应用[D].南昌:江西师范大学,2008.
[25]罗清君.逻辑代数系统的粗糙性与拓扑性质研究[D].西安:陕西师范大学,2014.
[26]熊金城.点集拓扑学[M].北京:高等教育出版社,2003.
[2]唐小娟,丁树良.粗糙集理论在认知诊断中的应用[J].心理科学,2016(4):790-795.
[3]王国虎,薛进学.基于粗糙集理论与支持向量机的多传感器信息融合方法[J].现代制造工程,2016(5):59-62.
[4]王永生.基于粗糙集理论的动态数据挖掘关键技术研究[D].北京:北京科技大学,2016.
[5]葛浩.基于粗糙集的不协调决策系统知识约简研究[D].合肥:安徽大学,2016.
[6]叶回春,张世文,黄远仿.粗糙集理论在土壤肥力评价指标权重确定中的应用[J].中国农业科技,2014,47(4):710-717.
[7]刘慧玲.基于粗糙集理论的齿轮箱故障诊断研究[D].太原:中北大学,2013.
[8]曹洪洋,任晓莹.基于粗糙集理论的区域降雨型滑坡预测预报[J].水文地质工程地质,2017(2).
[9]桑秀丽,李哲,肖汉杰.肿瘤病理类型绿色诊断方法研究——基于变精度粗糙集与贝叶斯网络[J].统计与信息论坛,2015(4):71-77.
[10]刘军凯,崔振新.基于粗糙集理论的飞机复飞事故影响因素分析[J].安全与环境工程,2017,24(2):172-177.
[11]Zhang Yanlan,Li Changqing.Relationships between generalized rough sets based on covering and reflexive neighborhood system[J].Information Sciences,2015,319:56-67.
[12]马周明,李进金.严格局部自反关系下的广义粗糙集[J].计算机工程与应用,2011,47(29):154-157.
[13]张宇.基于一般二元关系的几种粗糙集模型[D].辽宁锦州:渤海大学,2013.
[14]Pawlak Z.Rough sets:Theoretical aspects of reasoning about data[M].Boston:Kluwer Academic Publishers,1991.
[15]李招文,张珂.广义近似空间的拓扑结构[J].应用数学学报,2010,33(4):750-757.
[16]乔全喜.粗糙集的拓扑结构研究[D].成都:西南交通大学,2013.
[17]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.
[18]郑顶伟,蔡长勇.自反、传递(模糊)关系与拓扑空间[J].广西师范学院学报:自然科学版,2014,31(1):28-30.
[19]Yao Yiyu.Two views of the theory of rough sets in finite universes[J].International Journal of Approximate Reasoning,1996,15(4):291-317.
[20]Kondo M.On the structure of generalized rough sets[J].Information Sciences,2006,176:589-600.
[21]Qin Keyun.Generalized rough sets based on reflexive and transitive relations[J].Information Sciences,2008,178:4138-4141.
[22]Zhang Huapeng,Yao Ouyang,Wang Zhudeng.Note on“Generalized rough sets based on reflexive and transitive relations”[J].Information Sciences,2009,179(4):471-473.
[23]秦克云,裴峥,杜卫峰.粗糙近似算子的拓扑性质[J].系统工程学报,2006,21(1):81-85.
[24]吴志远.拓扑学在粗糙集理论中的应用[D].南昌:江西师范大学,2008.
[25]罗清君.逻辑代数系统的粗糙性与拓扑性质研究[D].西安:陕西师范大学,2014.
[26]熊金城.点集拓扑学[M].北京:高等教育出版社,2003.