计算机科学

计算机科学 ›› 2023, Vol. 50 ›› Issue (6): 122-130.doi: 10.11896/jsjkx.220800109

• 粒计算与知识发现 • 上一篇    下一篇

基于概念复合的对偶三支概念格及其概念约简

刘津1, 米据生1,2, 李仲玲1,2,3, 李美争4   

  1. 1 河北师范大学数学科学学院 石家庄 050024
    2 河北省计算数学与应用重点实验室(河北师范大学) 石家庄 050024
    3 河北师范大学汇华学院 石家庄 050024
    4 河北师范大学计算机与网络空间安全学院 石家庄 050024
  • 收稿日期:2022-08-11 修回日期:2022-11-27 出版日期:2023-06-15 发布日期:2023-06-06
  • 通讯作者: 米据生(mijsh@263.net)
  • 作者简介:(2878133706@qq.com)
  • 基金资助:
    国家自然科学基金(62076088,12101182,61502144);河北省高等学校科学技术研究项目(BJ2019014);河北省研究生创新资助项目(CXZZBS2022068)

Dual Three-way Concept Lattice Based on Composition of Concepts and Its Concept Reduction

LIU Jin1, MI Jusheng1,2, LI Zhongling1,2,3, LI Meizheng4   

  1. 1 College of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,China
    2 Hebei Key Laboratory of Computational Mathematics and Applications,Shijiazhuang 050024,China
    3 HuiHua College of Hebei Normal University,Shijiazhuang 050024,China
    4 College of Computer and Cyberspace Security,Hebei Normal University,Shijiazhuang 050024,China
  • Received:2022-08-11 Revised:2022-11-27 Online:2023-06-15 Published:2023-06-06
  • About author:LIU Jin,born in 1997,master.Her main research interests include concept lattice,granular computing and so on.MI Jusheng,born in 1966,Ph.D,second grade professor,Ph.D supervisor.His main research interests include rough set,concept lattice,granular computing,approximate reasoning and so on.
  • Supported by:
    National Natural Science Foundation of China(62076088,12101182, 61502144),Science and Technology Project of Hebei Education Department(BJ2019014) and Postgraduate Innovation Funding Project of Hebei Province(CXZZBS2022068).

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摘要： 三支概念格通过正负算子相结合,既表示出了共同拥有的信息,又表示出了共同不拥有的信息,是对经典概念格的扩展。但在处理一些实际问题时,人们也会从反向出发,考虑集合的补集可能不拥有的信息和可能拥有的信息,对偶三支概念格应运而生。文中提出了一种基于形式背景的对偶概念及其补背景中对偶概念的复合来构造对偶三支概念格的方法,经验证,通过概念复合方法得到的对偶三支概念与通过对偶三支算子得到的概念相同。进一步讨论了基于可辨识矩阵求解对偶三支概念格的属性约简方法,并借助此思想,给出了基于概念可辨识矩阵的对偶三支概念约简方法。

关键词: 概念格, 对偶三支概念, 属性约简, 概念约简, 辨识矩阵

Abstract: Three-way concept lattice not only represents the information jointly owned,but also represents the information that is not owned by each other by combining positive operators and negative operators.It is an extension of the classical concept lattice.However,when dealing with some practical problems,we sometimes start from the reverse,considering the information that the complementary sets may not have and the information that they may have,so the dual three-way concept lattice came into being.In this paper,a novel method to construct dual three-way concept lattices based on the composition of dual concepts in formal context and its complementary context is proposed.It is proved that the dual three-way concepts obtained by concepts composition are the same as those obtained by dual three-way operators.Then,we discuss the attribute reduction method of dual three-way concept lattices based on discernibility matrices.With the help of this idea,this paper proposes an approach to reducing the dual three-way concepts based on concept discernibility matrices.

Key words: Concept lattice, Dual three-way concept, Attribute reduction, Concept reduction, Discernibility matrix

中图分类号: 

  • TP18
[1]WILLE R.Restructuring Lattice Theory:An Approach Based on Hierarchies of Concepts [M].Ordered Sets,1982:445-470.
[2]GANTER B,WILLE R.Formal Concept Analysis:Mathematical Foundations [M].Berlin,Heidelberg:Springer,1999.
[3]MI J S,CHEN J K.Graph-based approaches for attribute reduction in Rough sets [J].Journal of Northwest University(Natural Science Edition),2019,49(4):508-516.
[4]ZHI H L,QI J J.Common-possible concept analysis:A granule description viewpoint [J].Applied Intelligence,2021,52(3):2975-2986.
[5]ZHI H L,QI J J,QIAN T,et al.Conflict analysis under one-vote veto based on approximate three-way concept lattice [J].Information Sciences,2020,516:316-330.
[6]LIAW T M,LIN S C.A general theory of concept lattice with tractable implication exploration [J].Theoretical Computer Science,2020,837:84-114.
[7]YAO Y Y.Three-way decisions with probabilistic rough sets[J].Information Sciences,2009,180(3):341-353.
[8]HAO F,YANG Y X,MIN G Y,et al.Incremental construction of three-way concept lattice for knowledge discovery in social networks [J].Information Science,2021,578:257-280.
[9]YANG S C,LU Y N,JIA X Y,et al.Constructing three-wayconcept lattice based on the composite of classical lattices [J].International Journal of Approximate Reasoning,2020,121:174-186.
[10]YAO Y Y.Interval sets and three-way concept analysis in incomplete contexts [J].International Journal of Machine Learning and Cybernetics,2017,8(1):3-20.
[11]WANG Z,WEI L,QI J J,et al.Attribute reduction of SE-ISI concept lattices for incomplete contexts [J].Soft Computing,2020,24(20):15143-15158.
[12]QI J J,QIAN T,WEI L.The connections between three-way and classical concept lattices [J].Knowledge-Based Systems,2016,91:143-151.
[13]MAO H,ZHAO S F,YANG L Z.Relationships between three-way concepts and classical concepts [J].Journal of Intelligent & Fuzzy Systems,2018,35(1):1063-1075.
[14]ZHAO X R,MIAO D Q,HU B Q.On relationship between three-way concept lattices [J].Information Sciences,2020,538:396-414.
[15]LONG B H,XUW H.Fuzzy three-way concept analysis and fuzzy three-way concept lattice [J].Journal of Nanjing University(Natural Science),2019,55(4):537-545.
[16]MAO H,CHENG Y L,LIU X Q.The relations between Fuzzy Three-way Concept Lattices and Fuzzy Concept Lattices [J].Fuzzy Systems and Mathematics,2020,34(6):167-174.
[17]SKOWRON A,RAUSZER C.The Discernibility Matrices andFunctions in Information Systems [M]//Intelligent Decision Support.1992.
[18]KONECNY J.On attribute reduction in concept lattices:Methods based on discernibility matrix are outperformed by basic clarification and reduction [J].Information Sciences,2017,415:199-212.
[19]WANG X,PENG Z H,LI J Y,et al.Method of Concept Reduction Based on Concept Discernibility Matrix [J].Computer Science,2021,48(1):125-130.
[20]WEI L,CAO L,QI J J,et al.Concept reduction and conceptcharacteristics in formal concept analysis [J].SCIENTIA SINICA Informationis,2020,50(12):1817-1833.
[21]REN R S,WEI L.The attribute reductions of three-way concept lattices [J].Knowledge- Based Systems,2016,99:92-102.
[22]MA J M,ZHANG W X.Axiomatic characterizations of dualconcept lattices [J].International Journal of Approximate Reasoning,2013,54(5):690-697.
[23]JIANG S R,YANG H Q,MI J S.Attribute Reduction in Dual Concept Lattices [J].Journal of Frontiers of Computer Science and Technology,2015,9(4):501-506.
[24]GUO Q C,MA J M.Judgment Methods of Interval-set Consistent Sets of Dual Interval-set Concept Lattices [J].Computer Science,2020,47(3):98-102.
[25]ZHI H L,QI J J,QIAN T,et al.Three-way dual concept analysis [J].International Journal of Approximate Reasoning,2019,114:151-165.
[26]YAO Y Y.A Comparative Study of Formal Concept Analysis and Rough Set Theory in Data Analysis[C]//Rough Sets and Current Trends in Computing.2004:59-68.
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