计算机科学

计算机科学 ›› 2024, Vol. 51 ›› Issue (7): 89-95.doi: 10.11896/jsjkx.230900009

• 数据库&大数据&数据科学 • 上一篇    下一篇

保持决策蕴涵不变的决策背景属性约简

毕盛, 翟岩慧, 李德玉   

  1. 山西大学计算机与信息技术学院 太原 030006
    山西大学计算智能与中文信息处理教育部重点实验室 太原 030006
  • 收稿日期:2023-09-04 修回日期:2023-12-01 出版日期:2024-07-15 发布日期:2024-07-10
  • 通讯作者: 翟岩慧(chai_yanhui@163.com)
  • 作者简介:(bisheng20210320@163.com)
  • 基金资助:
    国家自然科学基金(61972238,62072294)

Decision Implication Preserving Attribute Reduction in Decision Context

BI Sheng, ZHAI Yanhui, LI Deyu   

  1. School of Computer and Information Technology,Shanxi University,Taiyuan 030006,China
    Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education,Shanxi University,Taiyuan 030006,China
  • Received:2023-09-04 Revised:2023-12-01 Online:2024-07-15 Published:2024-07-10
  • About author:BI Sheng,born in 1999,postgraduate.His main research interests include data mining and intelligent decision.
    ZHAI Yanhui,born in 1981,associate professor,doctoral supervisor,is a re-gular member of CCF(No.22629M).His main research interests include concept lattice and knowledge reasoning.
  • Supported by:
    National Natural Science Foundation of China(61972238,62072294).

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摘要： 形式概念分析是一种利用概念格进行数据分析的理论,属性约简是概念格约简的主要方式之一。决策蕴涵是形式概念分析在决策情形下的一种知识表示与推理模型。在已有保持决策背景知识信息不变的属性约简研究中,通常以保持概念规则或粒规则来保持决策背景的知识信息。而相比于概念规则与粒规则,决策蕴涵具备更强的知识表示能力。为了进一步缩小数据在属性约简前后对知识信息表示的差异,对保持决策蕴涵不变的属性约简进行了研究。首先,结合决策蕴涵的语义给出了保持决策蕴涵不变的协调集和约简定义,提出了判定协调集和约简的充要条件;接着,通过实例分析了该约简存在的问题,并结合蕴涵理论给出解决方法,从而给出了弱协调集和弱约简的定义;然后,从知识包含的角度分析了弱约简相比于约简的合理性;最后,提出了判定弱协调集和弱约简的充要条件,并结合决策蕴涵规范基给出了能够找到弱约简的方法,丰富了保持知识信息的属性约简研究内容。

关键词: 形式概念分析, 属性约简, 决策蕴涵, 知识表示模型, 决策蕴涵规范基

Abstract: Formal concept analysis is a theory of data analysis using concept lattice,and attribute reduction is one of the main ways of concept lattice reduction.Decision implication is a knowledge representation and reasoning model of formal concept analysis in decision situations.In the existing research on attribute reduction that preserves decision context knowledge information,concept rules or granular rules are usually used to preserve decision context knowledge information.Compared with concept rules and granular rules,decision implication has a stronger ability of knowledge representation.To further reduce the difference between the representation of knowledge information before and after attribute reduction,a study is conducted on attribute reduction which preserves decision implication.Firstly,based on the semantics of decision implication,the definitions of consistent set and reduction that preserve decision implication aregiven,and the necessary and sufficient conditions for determining consistent set and reduction are provided.Examples show the problems of the reduction,and by combining implication theory,the definitions of weak consistent set and weak reduction are introduced.Then,the rationality of weak reduction compared with reduction is analyzed from the perspective of knowledge inclusion.Finally,the necessary and sufficient conditions for judging weak consistent set and weak reduction are provided,and the method that can find weak reduction is given by combining decision implication canonical basis,which enriches the research of attribute reduction that preserves knowledge information.

Key words: Formal concept analysis, Attribute reduction, Decision implication, Knowledge representation model, Decision implication canonical basis

中图分类号: 

  • TP182
[1]GANTER B,WILLE R.Formal Concept Analysis:Mathematical Foundations[M].Springer Science & Business Media,2012.
[2]YAN M Y,LI J H.Knowledge Discovery and Updating under the Evolution of Network Formal Contexts based on Three-Way Decision[J].Information Sciences,2022,601:18-38.
[3]YAO Y Y,QI J J,WEI L.Formal Concept Analysis,Rough Set Analysis and Granular Computing based on Three-Way Decisions[J].Journal of Northwest University(Natural Science Edition),2018,48(4):477-487.
[4]ZHAI Y H,QI J J,LI D Y,et al.The Structure Theorem ofThree-Way Concept Lattice[J].International Journal of Approximate Reasoning,2022,146:157-173.
[5]CHEN X,QI J J,ZHU X M,et al.Unlabelled Text MiningMethods based on Two Extension Models of Concept Lattices[J].International Journal of Machine Learning and Cybernetics,2020,11:475-490.
[6]MOTOGNA S,CRISTEA D,ŞOTROPA D,et al.Formal Concept Analysis Model for Static Code Analysis[J].Carpathian Journal of Mathematics,2022,38(1):159-168.
[7]ZHI H L,LI J H,LI Y N.Multilevel Conflict Analysis based on Fuzzy Formal Contexts[J].IEEE Transactions on Fuzzy Systems,2022,30(12):5128-5142.
[8]LI J H,WEI L,ZHANG Z,et al.Concept Lattice Theory and Method and Their Research Prospect[J].Pattern Recognition and Artificial Intelligence,2020,33(7):619-642.
[9]SHI L L,YANG H L.Object Granular Reduction of Fuzzy Formal Contexts[J].Journal of Intelligent & Fuzzy Systems,2018,34(1):633-644.
[10]SHAO M W,LI K W.Attribute Reduction in Generalized One-Sided Formal Contexts[J].Information Sciences,2017,378:317-327.
[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]REN R S,WEI L.The Attribute Reductions of Three-Way Con-cept Lattices[J].Knowledge-Based Systems,2016,99:92-102.
[13]LI Z L,MI J S,ZHANG T.An Updated Method of GranularReduct based on Cognitive Operators in Formal Contexts[J].International Journal of Approximate Reasoning,2023,154:72-83.
[14]YUE X W,PENG S,QIN K Y.Attribute Reduction Methods of Formal Context based on Object(Attribute) Oriented Concept Lattice[J].Computer Science,2020,47(S1):436-439.
[15]ZHAI Y H,LI D Y.Knowledge Structure Preserving Fuzzy Attribute Reduction in Fuzzy Formal Context[J].International Journal of Approximate Reasoning,2019,115:209-220.
[16]LI T J,XU Y C,WU W Z,et al.Attribute Reduction of Formal Contexts based on Decision Rules[J].Pattern Recognition and Artificial Intelligence,2017,30(9):769-778.
[17]ZHANG X H,MI J S,LI M Z.Attribute Reduction and Rule Fusion in Granular Consistent Formal Decision Contexts[J].CAAI Transactions on Intelligent Systems,2019,14(6):1138-1143.
[18]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.
[19]WEI L,CAO L,QI J J,et al.Concept Reduction and Characte-ristics in Formal Concept Analysis[J].Scientia Sinica(Informationis),2020,50(12):1817-1833.
[20]ZHAI Y H,LI D Y,QU K S.Decision Implications:ALogical Point of View[J].International Journal of Machine Learning and Cybernetics,2014,5(4):509-516.
[21]WANG Q,LI D Y,ZHAI Y H,et al.Parameterized Fuzzy Decision Implication[J].Journal of Computer Research and Development,2022,59(9):2066-2074.
[22]ZHAI Y H,JIA N,ZHANG S X,et al.Study on DeductionProcess and Inference Methods of Decision Implications[J].International Journal of Machine Learning and Cybernetics,2022,13(7):1959-1979.
[23]WU W Z,YEE L,MI J S.Granular Computing and Knowledge Reduction in Formal Contexts[J].IEEE Transactions on Knowledge and Data Engineering,2008,21(10):1461-1474.
[24]ZHANG S X,LI D Y,ZHAI Y H,et al.A Comparative Study of Decision Implication,Concept Rule and Granular Rule[J].Information Sciences,2020,508(C):33-49.
[25]ZHAI Y H,LI D Y,QU K S.Decision Implication Canonical Basis:ALogical Perspective[J].Journal of Computer and System Sciences,2015,81:208-218.
[26]ZHAI Y H,CHEN R J,LI D Y.An Update Method of Decision Implication Canonical Basis on Attribute Granulating[J].Intelligent Automation & Soft Computing,2023,37(2):1833-1851.
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