计算机科学 ›› 2022, Vol. 49 ›› Issue (3): 263-268.doi: 10.11896/jsjkx.210100204

• 人工智能 • 上一篇    下一篇

广义粗糙近似算子的拓扑性质

李妍妍, 秦克云   

  1. 西南交通大学数学学院 成都611756
  • 收稿日期:2021-01-26 修回日期:2021-06-10 出版日期:2022-03-15 发布日期:2022-03-15
  • 通讯作者: 秦克云(keyunqin@263.net)
  • 作者简介:(18839150213@163.com)
  • 基金资助:
    国家自然科学基金(61976130)

On Topological Properties of Generalized Rough Approximation Operators

LI Yan-yan, QIN Ke-yun   

  1. College of Mathematics,Southwest Jiaotong University,Chengdu 611756,China
  • Received:2021-01-26 Revised:2021-06-10 Online:2022-03-15 Published:2022-03-15
  • About author:LI Yan-yan,born in 1995,postgra-duate.Her main research interests include rough set theory and formal concept analysis.
    QIN Ke-yun,born in 1962,Ph.D,professor,Ph.D supervisor.His main research interests include rough set theory,formal concept analysis and fuzzy logic.
  • Supported by:
    National Natural Science Foundation of China(61976130).

摘要: 粗糙集理论是一种处理不确定性问题的数学工具。粗糙近似算子是粗糙集理论中的核心概念,基于等价关系的Pawlak粗糙近似算子可以推广为基于一般二元关系的广义粗糙近似算子。近似算子的拓扑结构是粗糙集理论的重点研究方向。文中主要研究基于一般二元关系的广义粗糙近似算子诱导拓扑的性质,给出了基于粒和基于子系统的广义粗糙近似算子诱导的4种拓扑,研究了它们之间的关系;通过对象的右邻域系统给出了基于粒的广义近似算子诱导的拓扑的基,研究了相应拓扑的正规性与正则性;通过分析基于子系统的广义上近似算子的性质,证明了基于子系统的广义上近似算子诱导的拓扑可以转化为基于对象的广义下近似算子诱导的拓扑。

关键词: 广义粗糙近似算子, 粒, 拓扑, 子系统

Abstract: Rough set theory is a mathematical tool for dealing with uncertain information.The core notions of rough set theory is approximation operators of approximation spaces.Pawlak approximation operators are established by using equivalence relations on the universe.They are extended to generalized rough approximation operators based on arbitrary binary relations.The topolo-gical structures of approximation operators are important topics in rough set theory.This paper is devoted to the study of topological properties of generalized rough approximation operators induced by arbitrary binary relations.Four types of topologies induced by generalized approximation operators based on granules and subsystems are presented and the relationships among these four types of topologies are discussed.The bases of the topologies induced by generalized approximation operators based on granules are presented by the right-neighborhood systems for objects,and the normality and regularity for related topologies are investigated.By analyzing the properties of the generalized upper approximation operators based on the subsystem,it is proved that the topologies induced by the subsystem-based generalized upper approximation operators can be transformed into the topologies induced by the generalized lower approximation operators based on the objects.

Key words: Generalized rough approximation operator, Granules, Subsystems, Topology

中图分类号: 

  • TP182
[1]PAWLAK Z.Rough sets [J].International Journal of Compu-ter & Information Sciences,1982,11:341-356.
[2]PAWLAK Z.Rough Sets:Theoretical Aspects of Reasoningabout Data [M].Kluwer Academic Publishers,Dordrecht & Boston,1991.
[3]POLKOWSKI L.Rough Sets [M].Physica-Verlag,Springer,2002.
[4]YAO Y Y.Constructive and algebraic methods of the theory of rough sets [J].Information Sciences,1998,109(1):21-47.
[5]MI J S,ZHANG W X.An axiomatic characterization of a fuzzy ge-neralization of rough sets [J].Information Sciences,2003,160(1):235-249.
[6]PAWLAK Z.Rough set approach to Knowledge-based decision [J].European Journal of Operational Research,1997,99:48-57.
[7]POMEROL J C.Artificial intelligence and human decision ma-king [J].European Journal of Operational Research,1997,99(1):3-25.
[8]WANG G Y.Rough set theory and knowledge acquisition [M].Xi’an:Xi’an Jiaotong University Press,2001.
[9]LIANG J Y,WANG J H,QIAN Y H.A new measure of uncertainty based on knowledge granulation for rough sets [J].Information Sciences,2008,179(4):458-470.
[10]YAO Y Y.Relational interpretations of neighborhood operators and rough set approximation operators [J].Information Sciences,1998,111(1):239-259.
[11]ZHANG W X,WU W Z,LIANG J Y,et al.Rough set theory and method [M].Beijing:Science Press,2001.
[12]LIU G L,ZHU K.The relationship among three types of rough approximation pairs [J].Knowledge-Based Systems,2014,60:28-34.
[13]KELLY J L.General Topology [M].Graduate Texts in Mathema-tics,Springer-VerlagNew York,1955:0072-5285.
[14]KONDO M.On the structure of generalizeed rough sets [J].Information Science,2006,176(5):589-600.
[15]QIN K Y,YANG J L,ZHENG P.Generalized rough sets based on reflexive and transitive relations [J].Information Science,2008,178(21):4138-4141.
[16]YAO Y Y.Two views of the theory of rough sets in finite universes [J].International Journal of Approximate Reasoning,1996,15:291-317.
[17]YU H,ZHAN W R.On the topological properties of generalized rough sets [J].Information Sciences,2014,263:141-152.
[18]ZHANG Y L,LI J J,LI C Q.Topological structure of relation-based generalized rough sets [J].Fundamenta Informaticae,2016,147(4):477-491.
[19]ZHANG Y L,LI C Q.Topological properties of a pair of relation-based approximation operators [J].Filomat,2017,31(19):6175-6183.
[20]WU H S,LIU G L.The relationships between topologies andgeneralized rough sets [J].International Journal of Approximate Reasoning,2020,119:313-324.
[21]ZHU W.Generalized rough sets based on relations [J].Information Science,2007,177(22):4997-5011.
[22]ZHU W.Topological approaches to covering rough sets [J].Information Science,2007,177(6):1499-1508.
[23]KORTELAINEN J.On the relationship between modified sets,topological spaces and rough sets [J].Fuzzy Sets and Systems,1994,61:91-95.
[24]YANG L Y,XU L S.Topological properties of generalized approximation spaces [J].Information Science,2011,181(17):3570-3580.
[25]ZHANG H P,YAO O Y,WANG Z D.Note on “generalized rough sets based on reflexive and transitive relations” [J].Information Sciences,2009,179(4):471-473.
[26]ZHAO Z G.On some types of covering rough sets from topolo-gical points of view[J].International Journal of Approximate Reasoning,2016,68:1-14.
[27]LIU G L,ZHENG H,ZOU J Y.Relations arising from coverings and their topological structures[J].International Journal of Approximate Reasoning,2017,80:348-358.
[28]WU Q E,WANG T,HUANG Y,et al.Topology theory onrough sets [J].IEEE Transactions on Systems,Man,and Cybernetics,2008,38(1):68-77.
[29]GRABOWSKI A.Topological interpretation of rough sets [J].Formalized Mathematics,2014,22(1):89-97.
[30]YANG M J,HUANG M Y,CHEN J.Multi-granularity neighborhood rough fuzzy sets and their uncertainty measurement [J].Journal of Chongqing University of Posts and Telecommunications (Natural Science Edition),2020,32(5):891-897.
[31]LU X,LI Y Y,QIN K Y.Relationship Among Three Types ofRough Approximation Pairs[J].Computer Science,2021,48(4):49-53.
[32]QIU J,LI L,MA Z M,et al.A note on the relationships between generalized rough sets and topologies[J].International Journal of Approximate Reasoning,2021,130:292-296.
[1] 唐清华, 王玫, 唐超尘, 刘鑫, 梁雯.
基于M2M相遇区的PDR室内定位方法
PDR Indoor Positioning Method Based on M2M Encounter Region
计算机科学, 2022, 49(9): 283-287. https://doi.org/10.11896/jsjkx.210800270
[2] 秦琪琦, 张月琴, 王润泽, 张泽华.
基于知识图谱的层次粒化推荐方法
Hierarchical Granulation Recommendation Method Based on Knowledge Graph
计算机科学, 2022, 49(8): 64-69. https://doi.org/10.11896/jsjkx.210600111
[3] 程富豪, 徐泰华, 陈建军, 宋晶晶, 杨习贝.
基于顶点粒k步搜索和粗糙集的强连通分量挖掘算法
Strongly Connected Components Mining Algorithm Based on k-step Search of Vertex Granule and Rough Set Theory
计算机科学, 2022, 49(8): 97-107. https://doi.org/10.11896/jsjkx.210700202
[4] 赵冬梅, 吴亚星, 张红斌.
基于IPSO-BiLSTM的网络安全态势预测
Network Security Situation Prediction Based on IPSO-BiLSTM
计算机科学, 2022, 49(7): 357-362. https://doi.org/10.11896/jsjkx.210900103
[5] 张源, 康乐, 宫朝辉, 张志鸿.
基于Bi-LSTM的期货市场关联交易行为检测方法
Related Transaction Behavior Detection in Futures Market Based on Bi-LSTM
计算机科学, 2022, 49(7): 31-39. https://doi.org/10.11896/jsjkx.210400304
[6] 曾志贤, 曹建军, 翁年凤, 蒋国权, 徐滨.
基于注意力机制的细粒度语义关联视频-文本跨模态实体分辨
Fine-grained Semantic Association Video-Text Cross-modal Entity Resolution Based on Attention Mechanism
计算机科学, 2022, 49(7): 106-112. https://doi.org/10.11896/jsjkx.210500224
[7] 许思雨, 秦克云.
基于剩余格的模糊粗糙集的拓扑性质
Topological Properties of Fuzzy Rough Sets Based on Residuated Lattices
计算机科学, 2022, 49(6A): 140-143. https://doi.org/10.11896/jsjkx.210200123
[8] 黄国兴, 杨泽铭, 卢为党, 彭宏, 王静文.
利用粒子滤波方法求解数据包络分析问题
Solve Data Envelopment Analysis Problems with Particle Filter
计算机科学, 2022, 49(6A): 159-164. https://doi.org/10.11896/jsjkx.210600110
[9] 周楚霖, 陈敬东, 黄凡.
基于无迹粒子滤波的WiFi-PDR融合室内定位技术
WiFi-PDR Fusion Indoor Positioning Technology Based on Unscented Particle Filter
计算机科学, 2022, 49(6A): 606-611. https://doi.org/10.11896/jsjkx.210700108
[10] 刘漳辉, 郑鸿强, 张建山, 陈哲毅.
多无人机使能移动边缘计算系统中的计算卸载与部署优化
Computation Offloading and Deployment Optimization in Multi-UAV-Enabled Mobile Edge Computing Systems
计算机科学, 2022, 49(6A): 619-627. https://doi.org/10.11896/jsjkx.210600165
[11] 周天清, 岳亚莉.
超密集物联网络中多任务多步计算卸载算法研究
Multi-Task and Multi-Step Computation Offloading in Ultra-dense IoT Networks
计算机科学, 2022, 49(6): 12-18. https://doi.org/10.11896/jsjkx.211200147
[12] 邱旭, 卞浩卜, 吴铭骁, 朱晓荣.
基于5G毫米波通信的高速公路车联网任务卸载算法研究
Study on Task Offloading Algorithm for Internet of Vehicles on Highway Based on 5G MillimeterWave Communication
计算机科学, 2022, 49(6): 25-31. https://doi.org/10.11896/jsjkx.211100198
[13] 傅思清, 黎铁军, 张建民.
面向粒子输运程序加速的体系结构设计
Architecture Design for Particle Transport Code Acceleration
计算机科学, 2022, 49(6): 81-88. https://doi.org/10.11896/jsjkx.210600179
[14] 方连花, 林玉梅, 吴伟志.
随机多尺度序决策系统的最优尺度选择
Optimal Scale Selection in Random Multi-scale Ordered Decision Systems
计算机科学, 2022, 49(6): 172-179. https://doi.org/10.11896/jsjkx.220200067
[15] 徐汝利, 黄樟灿, 谢秦秦, 李华峰, 湛航.
基于金字塔演化策略的彩色图像多阈值分割
Multi-threshold Segmentation for Color Image Based on Pyramid Evolution Strategy
计算机科学, 2022, 49(6): 231-237. https://doi.org/10.11896/jsjkx.210300096
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!