| 27 | 0 | 14 |
| 下载次数 | 被引频次 | 阅读次数 |
保持二元关系不变的概念约简是形式概念分析中的一个重要研究方向，可在不丢失原始信息的前提下仅选择一部分概念进行知识发现。一个形式背景的不同概念约简中的概念个数可能不同，其中概念个数最少的概念约简表明用最少的概念就能恢复原始背景的所有二元关系，可极大地简化知识表示方式。首先，给出形式背景的基与基数、最膨胀概念约简及最压缩概念约简的定义，并研究它们的性质；其次，研究形式背景的基与对象概念集(属性概念集)的关系，继而给出对象概念集(属性概念集)是基的等价刻画；最后，从形式背景的Ferrers维数与集合维数角度给出形式背景的基数范围。
Abstract：Concept reduction preserving binary relation is an important research direction in formal concept analysis, which allows for knowledge discovery by selecting some formal concepts(not all) without losing original information. The number of concepts in different concept reducts of a formal context may vary, where the concept reducts with the fewest number of formal concepts indicate that all binary relations can be recovered by the fewest formal concepts. This greatly simplifies the knowledge representation. We first define the bases and the cardinality of a formal context, the most expanded concept reducts and the most compressed concept reducts, and investigate their properties. Then, we explore the relationship between the bases of formal context and the set of object concepts(the set of attribute concepts), and provide an equivalent condition for when the set of object concepts(the set of attribute concepts) serves as a basis. Finally, we present the range of the cardinality of a formal context from the perspectives of the set dimension and the Ferrers dimension of a formal context.
[1] WILLE R.Restructuring lattice theory:An approach based on hierarchies of concepts [C]//Ordered Sets.Dordrecht-Boston:Springer,1982:445-470.
[2] GANTER B,WILLE R.Formal concept analysis:Mathematical foundations [M].Berlin Heidelberg:Springer-Verlag,1999:18-19,236-241.
[3] CARPINETO C,ROMANO G.Exploiting the potential of concept lattices for information retrieval with CERDO [J].Journal of Universal Computer Science,2004,10(8):985-1013.
[4] WILLE R.Why can concept lattices support knowledge discovery in databases?[J].Journal of Experimental and Theoretical Artificial Intelligence,2002,14(2):81-92.
[5] KUZNETSOV S O.Machine learning on the basis of formal concept analysis[J].Automation and Remote Control,2001,62(10):1543-1564.
[6] KHCHERIF R,GAMMOUDI M M,JAOUA A.Using difunctional relations in information organization[J].Information Sciences,2000,125:153-166.
[7] ELLOUMI S,FERJANI F,JAOUA A.Using minimal generators for composite isolated point extraction and conceptual binary relation coverage:Application for extracting relevant textual features [J].Information Sciences,2016,336:129-144.
[8] MOUAKHER A,BEN YAHIA S.QualityCover:Efficient binary relation coverage guided by induced knowledge quality [J].Information Sciences,2016,355:58-73.
[9] ELLOUMI S.A new approach for textual feature selection based on N-composite isolated labels [J].Natural Language Engineering,2020,26(2):221-243.
[10] 张文修，魏玲，祁建军.概念格的属性约简理论与方法 [J].中国科学E辑：信息科学，2005,35(6):628-639.ZHANG W X,WEI L,QI J J.Attribute reduction theory and approach to concept lattice [J].Science in China Series F-Information Sciences,2005,48(6):713-726.
[11] 魏玲，祁建军，张文修.决策形式背景的概念格属性约简 [J].中国科学E辑：信息科学，2008,38(2):195-208.WEI L,QI J J,ZHANG W X.Attribute reduction theory of concept lattice based on decision formal contexts [J].Science in China Series F-Information Sciences,2008,51(7):910-923.
[12] WU W Z,LEUNG Y,MI J S.Granular computing and knowledge reduction in formal contexts [J].IEEE Transactions on Knowledge and Data Engineering,2009,21(10):1461-1474.
[13] WANG X,ZHANG W X.Knowledge reduction in concept lattices based on irreducible elements [C]//Lecture Notes in Computer Science (Transactions on Computational Science V:Special Issue on Cognitive Knowledge Representation).Berlin,Heidelberg:Springer,2009,5540:128-142.
[14] LI T J,LI M Z,GAO Y.Attribute reduction of concept lattice based on irreducible elements [J].International Journal of Wavelets Multire-solution and Information Processing,2013,11(6):2792-2813.
[15] CORNEJO M E,MEDINA J,RAMIREZ-POUSSA E.Attribute reduction in multi-adjoint concept lattices [J].Information Sciences,2015,294:41-56.
[16] SHAO M W and LI K W.Attribute reduction in generalized one-sided formal contexts [J].Information Sciences,2017,378:317-327.
[17] REN R S,WEI L.The attribute reductions of three-way concept lattices [J].Knowledge-Based Systems,2016,99:92-102.
[18] BELOHLAVEK R,VYCHODIL V.On boolean factor analysis with formal concept as factors [J].In SCIS and ISIS,2006:1054-1059.
[19] BELOHLAVEK R,VYCHODIL V.Discovery of optimal factors in binary data via a novel method of matrix decomposition [J].Journal of Computer and System Sciences,2010,76(1):3-20.
[20] KEPRT A,SNASEL V.Binary factor analysis with help of formal concepts [C]//Proceedings of International Workshop on Concept Lattices and Their Applications.Ostrava:CEUR-WS.Org,2004,110:90-101.
[21] 魏玲，曹丽，祁建军，等.形式概念分析中的概念约简与概念特征[J].中国科学：信息科学，2020,50(12):1817-1833.WEI L,CAO L,QI J J,et al.Concept reduction and concept characteristics in formal concept analysis[J].Scientia Sinica Informationis,2020,50(12):1817-1833.
[22] 曹丽，魏玲，祁建军.保持二元关系不变的概念约简 [J].模式识别与人工智能，2018,31(6):516-524.CAO L,WEI L,QI J J.Concept reduction preserving binary relations [J].Pattern Recognition and Artificial Intelligence,2018,31(6):516-524.
[23] 谢小贤，李进金，陈东晓，等.基于布尔矩阵的保持二元关系不变的概念约简 [J].山东大学学报(理学版),2020,55(5):32-45.XIE X X,LI J J,CHEN D X,et al.Concept reduction of preserving binary relations based on boolean matrix [J].Journal of Shandong University (Natural Science Edition),2020,55(5):32-45.
[24] 王霞，彭致华，李俊余，等.一种基于概念可辨识矩阵的概念约简方法 [J].计算机科学，2021,48(1):125-130.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.
[25] 马文胜，侯锡林.形式概念分析中的同效关系与概念约简 [J].计算机科学，2023,50(4):63-76.MA W S,HOU X L.Same effect relation and concept reduction in formal concept analysis [J].Computer Science,2023,50(4):63-76.
[26] ZHAO S Y,QI J J,LI J A,et al.Concept reduction in formal concept analysis based on representative concept matrix[J].International Journal of Machine Learning and Cybernetics,2023,14(4):1147-1160.
[27] 魏玲，赵思雨，祁建军.对称形式背景及其概念约简 [J].西北大学学报(自然科学版),2023,53(5):794-802.WEI L,ZHAO S Y,QI J J.Symmetric formal context and its concept reduct [J].Journal of Northwest University (Natural Science Edition),2023,53(5):794-802.
[28] 朱朵朵，任睿思，赵思雨，等.基于不完备背景的3类SE-ISI概念约简 [J].西北大学学报(自然科学版),2023,53(5):821-829.ZHU D D,REN R S,ZHAO S Y,et al.Three types of SE-ISI concept reduction based on incomplete contexts [J].Journal of Northwest University (Natural Science Edition),2023,53(5):821-829.
[29] 李炎，赵思雨，任睿思，等.保持规则前件信息的概念约简 [J].西北大学学报(自然科学版),2023,53(5):803-811.LI Y,ZHAO S Y,REN R S,et al.Concept reduction preserving antecedent information of rules [J].Journal of Northwest University (Natural Science Edition),2023,53(5):803-811.
[30] J??KEL C,SCHMIDT S E.Packing problems,dimensions and the tensor product of complete lattices [C]//Proceedings of International Conference on Conceptual Structures.Bolzano,Italy:Springer,2021:142-151.
基本信息:
DOI：10.16152/j.cnki.xdxbzr.2026-01-013
中图分类号:TP18
引用信息:
[1]张琴,魏玲.形式背景的基与基数及其性质[J].西北大学学报(自然科学版),2026,56(01):141-150.DOI:10.16152/j.cnki.xdxbzr.2026-01-013.
基金信息:
国家自然科学基金(12171392); 陕西数理基础科学研究项目(23JSZ008)
2026-02-23
2026-02-23