计算机科学 ›› 2016, Vol. 43 ›› Issue (8): 216-222.doi: 10.11896/j.issn.1002-137X.2016.08.044

• 人工智能 • 上一篇    下一篇

基于属性消减的模糊概念格渐进式构造算法

王黎明,姜琴,张卓   

  1. 郑州大学信息工程学院 郑州450051,郑州大学信息工程学院 郑州450051,郑州大学信息工程学院 郑州450051
  • 出版日期:2018-12-01 发布日期:2018-12-01
  • 基金资助:
    本文受国家青年科学基金项目(61303044)资助

Incremental Algorithm for Constructing Fuzzy Concept Lattices Based on Attributes Decrement

WANG Li-ming, JIANG Qin and ZHANG Zhuo   

  • Online:2018-12-01 Published:2018-12-01

摘要: 当前模糊概念格的直接构造具有指数时间复杂度,且随着真值集合L大小的增加,模糊概念格的规模变得越来越庞大。为此提出了FMBUAD算法,它能够在原有模糊概念格的基础上消去多个消减属性(冗余或者无效属性)得到新的模糊概念格,且不考虑真值集合L的大小。基于模糊概念格的基础理论证明了FMBUAD算法的正确性。该算法首先将所有概念节点内涵中的消减属性隶属度移除;然后找出模糊概念格中所有的删除节点;最后集中处理删除节点父子节点之间的偏序关系。理论证明和实验结果表明:FMBUAD算法构造L-模糊概念格具有较好的时间性能。

关键词: 模糊概念格构造,消减属性,隶属度,广度优先,渐进式构造

Abstract: Constructing fuzzy lattices directly is always with an exponential time complexity currently.With the increase of the set of truth values L,the size of fuzzy concept lattice becomes larger and larger.This paper proposed an algorithm called FMBUAD.A new fuzzy concept lattice can be gotten by removing the membership degree of deleting attributes which become redundant and useless in original concepts,without reconstructing the fuzzy concept lattice from scratch and considering the set of truth values.We proved the correctness of FMBUAD based on the theoretical basis of fuzzy concept lattices.In order to update the original fuzzy concept lattice with the deleting attributes,FMBUAD removes the membership degree of deleting attributes of all concepts firstly.Secondly,it visits the fuzzy lattice to identify all of the nodes which have to be deleted.Finally,the algorithm has to deal with the partial order between the deleted nodes’s parents and children.The theory and experimental results show that FMBUAD has excellent performance for saving time.

Key words: Fuzzy concept lattice,Deleting attributes,Membership degree,Breadth first search,Incremental construction

[1] Ganter B,Wille R.Formal concept analysis.mathematical foundations[M].Berlin:Springer-Verlag,1999:66-68
[2] Chai Yu-mei,Zhang Zhuo,Wang Li-ming.An Algorithm forMining Global Closed Frequent Itemsets Based on Distributed Frequent Concept Direct Product[J].Chinese Journal of Computers,2012,35(5):990-1001(in Chinese) 柴玉梅,张卓,王黎明.基于频繁概念直乘分布的全局闭频繁项集挖掘算法[J].计算机学报,2012,35(5):990-1001
[3] Missaoui G R,Alaoui H.Incremental concept formation algorithms based on Galois (concept) lattices[J].Computational Intelligence,1995,11(2):246-267
[4] Bêlohlávek R.Fuzzy Galois Connections[J].Mathematical Logic Quarterly,1999,45(4):497-504
[5] Belohlavek R.Reduction and a simple proof of characterization of fuzzy concept lattices[J].Fundamenta Informaticae,2001,46(4):277-285
[6] Belohlavek R.Algorithms for fuzzy concept lattice[C]∥Proceedings of the 4th International Conference on Recent Advances in Soft Computing.Nottingham,United Kingdom,2002:200-205
[7] Belohlavek R,De Baets B,Outrata J,et al.Computing the Lat-tice of All Fixpoints of a Fuzzy Closure Operator[J].IEEE Transactions on Fuzzy Systems,2010,18(3):546-557
[8] Lindig C.Fast Concept Analysis[C]∥ Working with Conceptual Structures,2000.Aachen:Shaker Verlag,2000:152-161
[9] Pócs J.Note on generating fuzzy concept lattices via Galois connections[J].Information Sciences,2012,185(1):128-136
[10] Ghosh P,Kundu K,Sarkar D.Fuzzy graph representation of a fuzzy concept lattice[J].Fuzzy Sets and Systems,2010,161(12):1669-1675
[11] Pei D,Li M Z,Mi J S.Attribute reduction in fuzzy decision formal contexts[C]∥International Conference on Machine Lear-ning and Cybernetics (ICMLC).IEEE Press:New York,2011:204-208
[12] Aswanikumar C,Srinivas S.Concept lattice reduction using fuzzyK-Means clustering[J].Expert Systems with Applications,2010,37(3):2696-2704
[13] Li L,Zhang J.Attribute reduction in fuzzy concept lattices based on the T implication[J].Knowledge-Based Systems,2010,23(6):497-503
[14] Pang J,Zhang X,Xu W.Attribute Reduction in IntuitionisticFuzzy Concept Lattices[J].Abstract and Applied Analysis,2013,2013(54):1-13
[15] Zhang Lei,Zhang Hong-li,Yin Li-hua,et al.Theory and Algorithms of Attribute Decrement for Concept Lattice[J].Journal of Computer Research and Development,2013,50(2):248-259(in Chinese) 张磊,张宏莉,殷丽华,等.概念格的属性渐减原理与算法研究[J].计算机研究与发展,2013,50(2):248-259
[16] Zhang L,Zhang H,Shen X,et al.An Incremental Algorithm for Removing Object from Concept Lattice[J].Journal of Computational Information Systems,2013,9(9):3363-3372
[17] Zhang Zhou,Chai Yu-mei,Wang Li-ming,et al.A parallel algorithm generating fuzzy formal concepts[J].Pattern Recogniton and Artificial Intelligence,2013,26(3):260-269(in Chinese) 张卓,柴玉梅,王黎明,等.模糊形式概念并行构造算法[J].模式识别与人工智能,2013,26(3):260-269
[18] Zhang Zhuo,Du Juan,Wang Li-ming.Load balance-based algorithm for parallelly generating fuzzy formal concepts[J].Control and Decision,2014,29(11):1935-1942(in Chinese) 张卓,杜鹃,王黎明.基于负载均衡的模糊概念并行构造算法[J].控制与决策,2014,29(11):1935-1942
[19] Frank A,Asuncion A.UCI machine learning repository[EB/OL].http://www.ics.uci.edu

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