概念格理论与方法及其研究展望

doi:10.16451/j.cnki.issn1003-6059.202007005

Abstract
Figure/Table
References (244)
Related Citation (15)

Download: PDF (1362 KB) HTML (1 KB)
Export: BibTeX | EndNote (RIS)

Abstract

Concept lattice theory and method are the basic topics in the study of formal concept analysis, and important achievements are obtained. The previous study mainly focus on the generalization of concept lattice models, concept lattice construction, concept lattice reduction, concept lattice based rule acquisition, conceptual knowledge space, granular computing method for concept lattice and concept lattice applications. To further promote the study and the development of formal concept analysis theory, the existing research on theories and methods of concept lattice is summarized in detail, and an outlook is also produced for the researchers. Especially, it is pointed out that there are some key scientific problems in the above researches, a theoretical analysis of these problems is presented, and some preliminary research thoughts are provided as well. The obtained results offer a useful piece of advice for solving the problems in the future.

Key words： Concept Lattice Formal Concept Analysis Granular Computing Rough Set Three-Way Decision

Received: 15 June 2020

ZTFLH:

TP 18

Fund:

Supported by National Natural Science Foundation of China(No.11971211,61772021,61972238)

Corresponding Authors: LI Jinhai, Ph.D., professor. His research interests include cognitive computing, granular computing, big data analysis, concept lattice and rough set.

About author:: WEI Ling,Ph.D., professor. Her research interests include formal concept analysis, rough set and granular computing.ZHANG Zhuo, Ph.D., associate professor. His research interests include distributed artificial intelligence, and formal concept analysis and its application.ZHAI Yanhui, Ph.D., associate professor. His research interests include knowledge re-presentation and reasoning, granular computing and concept lattice.ZHANG Tao, Ph.D., associate professor. His research interests include concept lattice, granular computing and machine learning.ZHI Huilai, Ph.D., associate professor. His research interests include granular computing, formal concept analysis and rough set.MI Yunlong, Ph.D., lecturer. His research interests include data mining, neural network and formal concept analysis.

	Service

	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	LI Jinhai
	WEI Ling
	ZHANG Zhuo
	ZHAI Yanhui
	ZHANG Tao
	ZHI Huilai
	MI Yunlong

Cite this article:

LI Jinhai,WEI Ling,ZHANG Zhuo等. Concept Lattice Theory and Method and Their Research Prospect[J]. , 2020, 33(7): 619-642.

URL:

http://manu46.magtech.com.cn/Jweb_prai/EN/10.16451/j.cnki.issn1003-6059.202007005 OR http://manu46.magtech.com.cn/Jweb_prai/EN/Y2020/V33/I7/619

[1] WILLE R. Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts // RIVAL I, ed. Ordered Sets. Berlin, Germany: Springer, 1982: 445-470.
[2] ZADEH L A. Fuzzy Sets. Information and Control, 1965, 8(3): 338-353.
[3] PAWLAK Z. Rough Sets. International Journal of Computer and Information Sciences, 1982, 11(5): 341-356.
[4] ZADEH L A. Toward a Theory of Fuzzy Information Granulation and Its Centrality in Human Reasoning and Fuzzy Logic. Fuzzy Sets and Systems, 1997, 90(2): 111-127.
[5] YAO Y Y. Three-Way Decisions with Probabilistic Rough Sets. Information Sciences, 2010, 180(3): 341-353.
[6] GANTER B, WILLE R. Formal Concept Analysis: Mathematical Foundations. Berlin, Germany: Springer, 1999.
[7] CARPINETO C, ROMANO G. A Lattice Conceptual Clustering System and Its Application to Browsing Retrieval. Machine Learning, 1996, 24(2): 95-122.
[8] NGUYEN P H P, CORBETT D. A Basic Mathematical Framework for Conceptual Graphs. IEEE Transactions on Knowledge and Data Engineering, 2006, 18(2): 261-271.
[9] TU X D, WANG Y L, ZHANG M L, et al. Using Formal Concept Analysis to Identify Negative Correlations in Gene Expression Data. IEEE/ACM Transactions on Computational Biology and Bioinforma-tics, 2016, 13(2): 380-391.
[10] ZOU C F, ZHANG D Q, WAN J F, et al. Using Concept Lattice for Personalized Recommendation System Design. IEEE Systems Journal, 2017, 11(1): 305-314.
[11] SAMPATH S, SPRENKLE S, GIBSON E, et al. Applying Concept Analysis to User-Session-Based Testing of Web Applications. IEEE Transactions on Software Engineering, 2007, 33(10): 643-658.
[12] 陈德刚,徐伟华,李金海,等.粒计算基础教程.北京:科学出版社, 2019.
(CHEN D G, XU W H, LI J H, et al. Elements of Granular Computing. Beijing, China: Science Press, 2019.)
[13] MEDINA J. Relating Attribute Reduction in Formal, Object-Oriented and Property-Oriented Concept Lattices. Computers and Mathematics with Applications, 2012, 64(6): 1992-2002.
[14] BURUSCO A, FUENTES-GONZALEZ R. The Study of the L-Fuzzy Concept Lattice. Mathware and Soft Computing, 1994, 1(3): 209-218.
[15] BELOHLÁVEK R. Fuzzy Galois Connections. Mathematical Logic Quarterly, 1999, 45(4): 497-504.
[16] DUNTSCH I, GEDIGA G. Modal-Style Operators in Qualitative Data Analysis // Proc of the IEEE International Conference on Data Mining. Washington, USA: IEEE, 2002: 155-162.
[17] YAO Y Y. Concept Lattices in Rough Set Theory // Proc of the IEEE Annual Meeting of Fuzzy Information. Washington, USA: IEEE, 2004: 796-801.
[18] QI J J, WEI L, YAO Y Y. Three-Way Formal Concept Analysis // Proc of the International Conference on Rough Sets and Know-ledge Technology. Berlin, Germany: Springer, 2014: 732-741.
[19] LEHMANN F, WILLE R. A Triadic Approach to Formal Concept Analysis // Proc of the 3rd International Conference on Conceptual Structures. Berlin, Germany: Springer, 1995: 32-43.
[20] DJOUADI Y, PRADE H. Interval-Valued Fuzzy Formal Concept Analysis // Proc of the International Symposium on Methodologies for Intelligent Systems. Berlin, Germany: Springer, 2009: 592-601.
[21] JAOUA A, ELLOUMI S. Galois Connection, Formal Concepts and Galois Lattice in Real Relations: Application in a Real Classifier. Journal of Systems and Software, 2002, 60(2): 149-163.
[22] GODIN R, MISSAOUI R, ALAOUI H. Incremental Concept Formation Algorithms Based on Galois(Concept) Lattices. Computational Intelligence, 1995, 11(2): 246-267.
[23] VALTCHEV P, MISSAOUI R, LEBRUN P. A Partition-Based Approach towards Constructing Galois(Concept) Lattices. Discrete Mathematics, 2002, 256(3): 801-829.
[24] FU H G, NGUIFO E M. A Parallel Algorithm to Generate Formal Concepts for Large Data // Proc of the 2nd International Conference on Formal Concept Analysis. Berlin, Germany: Springer, 2004: 394-401.
[25] 张文修,魏玲,祁建军.概念格的属性约简理论与方法.中国科学(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. Science in China(Information Sciences), 2005, 35(6): 628-639.)
[26] WU W Z, LEUNG Y, MI J S. Granular Computing and Knowledge Reduction in Formal Contexts. IEEE Transactions on Knowledge and Data Engineering, 2009, 21(10): 1461-1474.
[27] STUMME G, TAOUIL R, BASTIDE Y, et al. Computing Iceberg Concept Lattices with Titanic. Data and Knowledge Engineering, 2002, 42(2): 189-222.
[28] 张文修,仇国芳.基于粗糙集的不确定决策.北京:清华大学出版社, 2005.
(ZHANG W X, QIU G F. Uncertain Decision Making Based on Rough Sets. Beijing, China: Tsinghua University Press, 2005.)
[29] LI J H, MEI C L, LÜ Y J. A Heuristic Knowledge-Reduction Method for Decision Formal Contexts. Computers and Mathematics with Applications, 2011, 61(4): 1096-1106.
[30] LI J H, MEI C L, LÜ Y J. Knowledge Reduction in Decision Formal Contexts. Knowledge-Based Systems, 2011, 24(5): 709-715.
[31] SHI Y, MI Y L, LI J H, et al. Concurrent Concept-Cognitive Lear-ning Model for Classification. Information Sciences, 2019, 496: 65-81.
[32] LI J H, MEI C L, XU W H, et al. Concept Learning via Granular Computing: A Cognitive Viewpoint. Information Sciences, 2015, 298: 447-467.
[33] MI Y L, SHI Y, LI J H, et al. Fuzzy-Based Concept Learning Method: Exploiting Data with Fuzzy Conceptual Clustering [J/OL]. [2020-04-07]. https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9058987.
[34] SHI Y, MI Y L, LI J H, et al. Concept-Cognitive Learning Model for Incremental Concept Learning [J/OL]. [2020-04-07]. https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=8574051.
[35] WEI L, WAN Q. Granular Transformation and Irreducible Elements Judgment Based on Pictorial Diagrams. IEEE Transactions on Cybernetics, 2016, 46(2): 380-387.
[36] XU W H, LI W T. Granular Computing Approach to Two-Way Learning Based on Formal Concept Analysis in Fuzzy Datasets. IEEE Transactions on Cybernetics, 2016, 46(2): 366-379.
[37] MA J M, ZHANG W X, LEUNG Y, et al. Granular Computing and Dual Galois Connection. Information Sciences, 2007, 177 (23): 5365-5377.
[38] KANG X P, LI D Y, WANG S G, et al. Formal Concept Analysis Based on Fuzzy Granularity Base for Different Granulations. Fuzzy Sets and Systems, 2012, 203: 33-48.
[39] SHAO M W, LEUNG Y, WANG X Z, et al. Granular Reducts of Formal Fuzzy Contexts. Knowledge-Based Systems, 2016, 114: 156-166.
[40] 李金海,吴伟志.形式概念分析的粒计算方法及其研究展望.山东大学学报(理学版), 2017, 52(7): 1-12.
(LI J H, WU W Z. Granular Computing Approach for Formal Concept Analysis and Its Research Outlooks. Journal of Shandong University (Natural Science), 2017, 52(7): 1-12.)
[41] ZHI H L, LI J H. Granule Description Based on Formal Concept Analysis. Knowledge-Based Systems, 2016, 104: 62-73.
[42] 苗夺谦,张清华,钱宇华,等.从人类智能到机器实现模型——粒计算理论与方法.智能系统学报, 2016, 11(6): 743-757.
(MIAO D Q, ZHANG Q H, QIAN Y H, et al. From Human Inte-lligence to Machine Implementation Model: Theories and Applications Based on Granular Computing. CAAI Transactions on Intelligent Systems, 2016, 11(6): 743-757.)
[43] 梁吉业,钱宇华,李德玉,等.大数据挖掘的粒计算理论与方法.中国科学(信息科学), 2015, 45(11): 1355-1369.
(LIANG J Y, QIAN Y H, LI D Y, et al. Theory and Method of Granular Computing for Big Data Mining. Science in China(Information Sciences), 2015, 45(11): 1355-1369.)
[44] 徐计,王国胤,于洪.基于粒计算的大数据处理.计算机学报, 2015, 38(8): 1497-1517.
(XU J, WANG G Y, YU H. Review of Big Data Processing Based on Granular Computing. Chinese Journal of Computers, 2015, 38(8): 1497-1517.)
[45] KUZNETSOV S O. Complexity of Learning in Concept Lattices from Positive and Negative Examples. Discrete Applied Mathema-tics, 2004, 142(1/2/3): 111-125.
[46] 范世青,张文修.模糊概念格与模糊推理.模糊系统与数学, 2006, 20(1): 11-17.
(FAN S Q, ZHANG W X. Fuzzy Concept Lattice and Fuzzy Reasoning. Fuzzy Systems and Mathematics, 2006, 20(1): 11-17.)
[47] GEORGESCU G, POPESCU A. Non-Dual Fuzzy Connections. Archive for Mathematical Logic, 2004, 43(8): 1009-1039.
[48] 杨丽,徐杨.基于格值逻辑的模糊概念格.模糊系统与数学, 2009, 23(5): 15-20.
(YANG L, XU Y. Fuzzy Concept Lattice Based on Lattice-Valued Logic. Fuzzy Systems and Mathematics, 2009, 23(5): 15-20.)
[49] MEDINA J, OJEDA-ACIEGO M. Multi-adjoint t-Concept Latti-ces. Information Sciences, 2010, 180(5): 712-725.
[50] ELLOUMI S, JAAM J, HASNAH A, et al. A Multi-level Conceptual Data Reduction Approach Based on the Lukasiewicz Implication. Information Sciences, 2004, 163(4): 253-262.
[51] ZHANG W X, MA J M, FAN S Q. Variable Threshold Concept Lattices. Information Sciences, 2007, 177(22): 4883-4892.
[52] LI L F, ZHANG J K. Attribute Reduction in Fuzzy Concept La-ttices Based on the T Implication. Knowledge-Based Systems, 2010, 23(6): 497-503.
[53] BELOHLAVEK R. A Note on Variable Threshold Concept La-ttices: Threshold-Based Operators are Reducible to Classical Concept-Forming Operators. Information Sciences, 2007, 177(15): 3186-3191.
[54] BÉLOHLÁVEK R, SKLENÁR\/ V, ZACKPAL J. Crisply Generated Fuzzy Concepts // Proc of the 3rd International Conference on Formal Concept Analysis. Berlin, Germany: Springer, 2005: 269-284.
[55] LI J H, MEI C L, LÜ Y J. Incomplete Decision Contexts: Appro-ximate Concept Construction, Rule Acquisition and Knowledge Reduction. International Journal of Approximate Reasoning, 2013, 54(1): 149-165.
[56] YAO Y Y. Interval Sets and Three-Way Concept Analysis in Incomplete Contexts. International Journal of Machine Learning and Cybernetics, 2017, 8(1): 3-20.
[57] DEOGUN J S, SAQUER J. Monotone Concepts for Formal Concept Analysis. Discrete Applied Mathematics, 2004, 144(1/2): 70-78.
[58] WANG L D, LIU X D. Concept Analysis via Rough Set and AFS Algebra. Information Sciences, 2008, 178(21): 4125-4137.
[59] 龙柄翰,徐伟华.模糊三支概念分析与模糊三支概念格.南京大学学报(自然科学版), 2019, 54(4): 537-545.
(LONG B H, XU W H. Fuzzy Three-Way Concept Analysis and Fuzzy Three-way Concept Lattice. Journal of Nanjing University (Natural Science), 2019, 54(4): 537-545.)
[60] GANTER B, KUZNETSOV S O. Pattern Structures and Their Projections // Proc of the International Conference on Conceptual Structures. Berlin, Germany: Springer, 2001: 129-142.
[61] KUZNETSOV S O. Learning of Simple Conceptual Graphs from Positive and Negative Examples // Proc of the European Confe-rence on Principles of Data Mining and Knowledge Discovery. Berlin, Germany: Springer, 1999: 384-391.
[62] BORDAT J P. Calcul Pratique du Treillis de Galois d′une Correspondance. Mathmatiques et Sciences Humaines, 1986, 96: 31-47.
[63] NOURINE L, RAYNAUD O. A Fast Algorithm for Building La-ttices. Information Processing Letters, 1999, 71(5/6): 199-204.
[64] LINDIG C. Fast Concept Analysis // Proc of the 8th International Conference on Conceptual Structures. Berlin, Germany: Springer, 2000: 152-161.
[65] VALTCHEV P, MISSAOUI R. Building Concept (Galois) Lattices from Parts: Generalizing the Incremental Methods // Proc of the 9th International Conference on Conceptual Structures. Berlin, Germany: Springer, 2001: 290-303.
[66] CHOI V. Faster Algorithms for Constructing a Concept (Galois) Lattice[C/OL]. [2020-04-07]. https://arxiv.org/pdf/cs/0602069.pdf.
[67] VAN DER MERWE D, OBIEDKOV S, KOURIE D. AddIntent: A New Incremental Algorithm for Constructing Concept Lattices // Proc of the International Conference on Formal Concept Analysis. Berlin, Germany: Springer, 2004: 372-385.
[68] ANDREWS S. In-Close, A Fast Algorithm for Computing Formal Concepts // Proc of the 17th International Conference on Conceptual Structures. Berlin, Germany: Springer, 2009: 1-14.
[69] NJIWOUA P, NGUIFO E M. A Parallel Algorithm to Build Concept Lattice // Proc of the 4th Groningen International Information Technology Conference for Students. Fevrier, The Netherlands: University of Groningen Press, 1997: 103-107.
[70] KENGUE J F D, VALTCHEV P, FJAMEGNI C T. A Parallel Algorithm for Lattice Construction // Proc of the International Confe-rence on Formal Concept Analysis. Berlin, Germany: Springer, 2005: 249-264.
[71] KRAJCA P, OUTRATA J, VYCHODIL V. Parallel Algorithm for Computing Fixpoints of Galois Connections. Annals of Mathematics and Artificial Intelligence, 2010, 59(2): 257-272.
[72] OUTRATA J, VYCHODIL V. Fast Algorithm for Computing Fixpoints of Galois Connections Induced by Object-Attribute Relational Data. Information Sciences, 2012, 185(1): 114-127.
[73] OUTRATA J. A Lattice-Free Concept Lattice Update Algorithm Based on *CbO // Proc of the 10th International Conference on Concept Lattices and Their Applications. Berlin, Germany: Springer, 2013: 261-274.
[74] MUANGPRATHUB J. A Novel Algorithm for Building Concept La-ttice. Applied Mathematical Sciences, 2014, 8(11): 507-515.
[75] AMRANE B, BELALEM G, BRANCI S, et al. Efficient Incremental Algorithm for Building Swiftly Concepts Lattices. International Journal of Web Portals, 2014, 6(1): 21-34.
[76] 齐红,刘大有,胡成全,等.基于搜索空间划分的概念生成算法.软件学报, 2005, 16(12): 2029-2035.
(QI H, LIU D Y, HU C Q, et al. An Algorithm for Generating Concepts Based on Search Space Partition. Journal of Software, 2005, 16(12): 2029-2035.)
[77] 张继福,张素兰,胡立华.约束概念格及其构造方法.智能系统学报, 2006, 1(2): 31-38.
(ZHANG J F, ZHANG S L, HU L H. Constrained Concept La-ttice and Its Construction Method. CAAI Transactions on Intelligent Systems, 2006, 1(2): 31-38.)
[78] 杜秋香,张继福,张素兰.概念格特化的概念格更新构造算法.智能系统学报, 2008, 3(5): 443-448.
(DU Q X, ZHANG J F, ZHANG S L. An Improved Algorithm Based on Concept Specialization for Constructing Concept Lattices. CAAI Transactions on Intelligent Systems, 2008, 3(5): 443-448.)
[79] 董辉,马垣,宫玺.一种新的概念格并行构造算法.计算机科学与探索, 2008, 2(6): 651-657.
(DONG H, MA Y, GONG X. A New Parallel Algorithm for Construction of Concept Lattice. Journal of Frontiers of Computer Science and Technology, 2008, 2(6): 651-657.)
[80] 智慧来,智东杰,刘宗田.概念格合并原理与算法.电子学报, 2010, 38(2): 455-459.
(ZHI H L, ZHI D J, LIU Z T. Theory and Algorithm of Concept Lattice Union. Acta Electronica Sinica, 2010, 38(2): 455-459.)
[81] ZHI H L, LI J H. Influence of Dynamical Changes on Concept La-ttice and Implication Rules. International Journal of Machine Learning and Cybernetics, 2018, 9(5): 795-805.
[82] 姜琴,张卓,王黎明.基于多属性同步消减的概念格构造算法.小型微型计算机系统, 2016, 37(4): 646-652.
(JIANG Q, ZHANG Z, WANG L M. Algorithms of Constructing Concept Lattice Based on Deleting Multiple Attributes Synchronously. Journal of Chinese Computer Systems, 2016, 37(4): 646-652.)
[83] 张涛,白冬辉,李慧.属性拓扑的并行概念计算算法.软件学报, 2017, 28(12): 3129-3145.
(ZHANG T, BAI D H, LI H. Parallel Concept Computing Based on Bottom-up Decomposition of Attribute Topology. Journal of Software, 2017, 28(12): 3129-3145.)
[84] 蔡勇,陈红梅.MapReduce环境下基于概念分层的概念格并行构造算法.中国科学技术大学学报, 2018, 48(4): 275-283.
(CAI Y, CHEN H M. A Parallel Algorithm for Constructing Concept Lattice Based on Hierarchical Concept under MapReduce. Journal of University of Science and Technology of China, 2018, 48(4): 275-283.)
[85] BÉLOHLÁVEK R, VYCHODIL V. What Is a Fuzzy Concept La-ttice[C/OL]. [2020-04-07]. https://pdfs.semanticscholar.org/df4c/eed281d70fe1aa2b9f481ce8a1912d44fcb6.pdf.
[86] PÓCS J. Note on Generating Fuzzy Concept Lattices via Galois Connections. Information Sciences, 2012, 185(1): 128-136.
[87] CROSS V, KANDASAMY M, YI W T. Comparing Two Approaches to Creating Fuzzy Concept Lattices // Proc of the Annual Meeting of the North American on Fuzzy Information Processing Society. Washington, USA: IEEE, 2011. DOI: 10.1109/NAFIPS.2011.5752007.
[88] THO Q T, HUI S C, FONG A C M, et al. Automatic Fuzzy Onto-logy Generation for the Semantic Web. IEEE Transactions on Knowledge and Data Engineering, 2006, 18(6): 842-856.
[89] 许佳卿,彭鑫,赵文耘.一种基于模糊概念格和代码分析的软件演化分析方法.计算机学报, 2009, 32(9): 1832-1844.
(XU J Q, PENG X, ZHAO W Y. An Evolution Analysis Method Based on Fuzzy Concept Lattice and Source Code Analysis. Chinese Journal of Computers, 2009, 32(9): 1832-1844.)
[90] DE MAIO C, FENZA G, LOIA V, et al. Towards an Automatic Fuzzy Ontology Generation // Proc of the IEEE International Conference on Fuzzy Systems. Washington, USA: IEEE, 2009: 1044-1049.
[91] 刘宗田,强宇,周文,等.一种模糊概念格模型及其渐进式构造算法.计算机学报, 2007, 30(2): 184-188.
(LIU Z T, QIANG Y, ZHOU W, et al. A Fuzzy Concept Lattice Model and Its Incremental Construction Algorithm. Chinese Journal of Computers, 2007, 30(2): 184-188.)
[92] BÉLOHLÁVEK R. What Is a Fuzzy Concept Lattice? II // Proc of the 13th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing. Berlin, Germany: Springer, 2011: 19-26.
[93] BÉLOHLÁVEK R, DE BAETS B, OUTRATA B, et al. Computing the Lattice of All Fixpoints of a Fuzzy Closure Operator. IEEE Transactions on Fuzzy Systems, 2010, 18(3): 546-557.
[94] BÉLOHLÁVEK R. Algorithms for Fuzzy Concept Lattices // Proc of the 4th International Conference on Recent Advances in Soft Computing. Berlin, Germany: Springer, 2002: 200-205.
[95] BÉLOHLÁVEK R. OUTRATA J, VYCHODIL V. Direct Factorization by Similarity of Fuzzy Concept Lattice by Factorization of Input Data // Proc of the 4th International Conference on Concept Lattices and Their Applications. Berlin, Germany: Springer, 2006: 68-79.
[96] BÉLOHLÁVEK R. DVO?ÁK J, OUTRATA J. Fast Factorization by Similarity in Formal Concept Analysis of Data with Fuzzy Attri-butes. Journal of Computer and System Sciences, 2007, 73(6):1012-1022.
[97] 张卓,柴玉梅,王黎明,等.模糊形式概念并行构造算法.模式识别与人工智能, 2013, 26(3): 260-269.
(ZHANG Z, CHAI Y M, WANG L M, et al. A Parallel Algorithm Generating Fuzzy Formal Concepts. Pattern Recognition and Artificial Intelligence, 2013, 26(3): 260-269.)
[98] 张卓,杜鹃,王黎明.基于负载均衡的模糊概念并行构造算法.控制与决策, 2014, 29(11): 1935-1942.
(ZHANG Z, DU J, WANG L M. Load Balance-Based Algorithm for Parallelly Generating Fuzzy Formal Concepts. Control and Decision, 2014, 29(11): 1935-1942.)
[99] ZHANG Z. Constructing L-Fuzzy Concept Lattices without Fuzzy Galois Closure Operation. Fuzzy Sets and Systems, 2018, 333: 71-86.
[100] ROUANE M H, NEHME K, VALTCHEV P, et al. On-Line Maintenance of Iceberg Concept Lattices // Proc of the 12th International Conference on Conceptual Structures. Berlin, Germany: Springer, 2004: 1-14.
[101] NEHMÉ K, VALTCHEV P, ROUANE M H, et al. On Computing the Minimal Generator Family for Concept Lattices and Icebergs // Proc of the International Conference on Formal Concept Analysis. Berlin, Germany: Springer, 2005: 192-207.
[102] ZAKI M J, HSIAO C J. Efficient Algorithms for Mining Closed Itemsets and Their Lattice Structure. IEEE Transactions on Knowledge and Data Engineering, 2005, 17(4): 462-478.
[103] HU X G, LIU W, WANG D X, et al. Mining Frequent Itemsets Using a Pruned Concept Lattice // Proc of the 4th International Conference on Fuzzy Systems and Knowledge Discovery. Wa-shington, USA: IEEE, 2007. DOI: 10.1109/FSKD.2007.401.
[104] 王黎明,张卓.基于iceberg概念格并置集成的闭频繁项集挖掘算法.计算机研究与发展, 2007, 44(7): 1184-1190.
(WANG L M, ZHANG Z. An Algorithm for Mining Closed Frequent Itemsets Based on Apposition Assembly of Iceberg Concept Lattices. Journal of Computer Research and Development, 2007, 44(7): 1184-1190.)
[105] 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.计算机学报, 2012, 35(5): 990-1001.
(CHAI Y M, ZHANG Z, WANG L M. An Algorithm for Mining Global Closed Frequent Itemsets Based on Distributed Frequent Concept Direct Product. Chinese Journal of Computers, 2012, 35(5): 990-1001.)
[106] LA P T, LE B, VO B. Incrementally Building Frequent Closed Itemset Lattice. Expert Systems with Applications, 2014, 41(6): 2703-2712.
[107] GUPTA A, BHATNAGAR V, KUMAR N. Mining Closed Itemsets in Data Stream Using Formal Concept Analysis // Proc of the International Conference on Data Warehousing and Knowledge Discovery. Berlin, Germany: Springer, 2010: 285-296.
[108] KOVÁCS L, GÁBOR S. Generalization of String Transformation Rules Using Optimized Concept Lattice Construction Method. Procedia Engineering, 2017, 181: 604-611.
[109] WILLE R. The Basic Theorem of Triadic Concept Analysis. Order, 1995, 12(2): 149-158.
[110] OSICKA P. Algorithms for Computation of Concept Trilattice of Triadic Fuzzy Context // Proc of the International Conference on Information Processing and Management of Uncertainty in Know-ledge-Based Systems. Berlin, Germany: Springer, 2012: 221-230.
[111] BÉLOHLÁVEK R, OSICKA P. Triadic Concept Lattices of Data with Graded Attributes. International Journal of General Systems, 2012, 41(2): 93-108.
[112] BÉÁVEK R, OSICKA P. Triadic Fuzzy Galois Connections as Ordinary Connections. Fuzzy Sets and Systems, 2014, 249: 83-99.
[113] 魏玲,万青,钱婷,等.三元概念分析综述.西北大学学报(自然科学版), 2014, 44(5): 689-699.
(WEI L, WAN Q, QIAN T, et al. An Overview of Triadic Concept Analysis. Journal of Northwest University(Natural Science Edition), 2014, 44(5): 689-699.)
[114] 汤亚强,范敏,李金海.三元形式概念分析下的认知系统模型及信息粒转化方法.山东大学学报(理学版), 2014, 49(8): 102-106.
(TANG Y Q, FAN M, LI J H. Cognitive System Model and Approach to Transformation of Information Granules under Triadic Formal Concept Analysis. Journal of Shandong University(Natural Science), 2014, 49(8): 102-106.)
[115] 王冰洁,张卓,王黎明.概念三元格渐进式构造算法.小型微型计算机系统, 2017, 38(9): 2101-2106.
(WANG B J, ZHANG Z, WANG L M. Incremental Algorithm for Constructing Concept Trilattices. Journal of Chinese Computer Systems, 2017, 38(9): 2101-1206.)
[116] 王霞,江山,李俊余,等.三元概念的一种构造方法.计算机研究与发展, 2019, 56(4): 844-853.
(WANG X, JIANG S, LI J Y, et al. A Construction Method of Triadic Concepts. Journal of Computer Research and Development, 2019, 56(4): 844-853.)
[117] WEI L, QIAN T, WAN Q, et al. A Research Summary about Triadic Concept Analysis. International Journal of Machine Lear-ning and Cybernetics, 2018, 9(4): 699-712.
[118] LI J H, MEI C L, WANG J H, et al. Rule-Preserved Object Compression in Formal Decision Contexts Using Concept Lattices. Knowledge-Based Systems, 2014, 71: 435-445.
[119] TRNECKA M, TRNECKOVA M. Data Reduction for Boolean Matrix Factorization Algorithms Based on Formal Concept Analysis. Knowledge-Based Systems, 2018, 158: 75-80.
[120] 魏玲.粗糙集与概念格约简理论与方法.博士学位论文.西安:西安交通大学, 2005.
(WEI L. Reduction Theory and Approach to Rough Set and Concept Lattice. Xi′an, China: Xi′an Jiaotong University, 2005.)
[121] WANG X, MA J M. A Novel Approach to Attribute Reduction in Concept Lattices // Proc of the International Conference on Rough Sets and Knowledge Technology. Berlin, Germany: Springer, 2006: 522-529.
[122] MI J S, LEUNG Y, WU W Z. Approaches to Attribute Reduction in Concept Lattices Induced by Axialities. Knowledge-Based Systems, 2010, 23(6): 504-511.
[123] LI T J, LI M Z, GAO Y. Attribute Reduction of Concept Lattice Based on Irreducible Elements. International Journal of Wavelets Multiresolution and Information Processing, 2013, 11(6): 2792-2813.
[124] 魏玲,祁建军,张文修.决策形式背景的概念格属性约简.中国科学(信息科学), 2008, 38(2): 195-208.
(WEI L, QI J J, ZHANG W X. Attribute Reduction and Rules Extraction in Decision Formal Context Based on Concept Lattice. Science in China(Information Sciences), 2008, 38(2): 195-208.)
[125] LI J H, MEI C L, LÜ Y J. Knowledge Reduction in Formal Decision Contexts Based on an Order-Preserving Mapping. International Journal of General Systems, 2012, 41(2): 143-161.
[126] LI J H, MEI C L, LÜ Y J. Knowledge Reduction in Real Decision Formal Contexts. Information Sciences, 2012, 189: 191-207.
[127] SHAO M W, LI K W. Attribute Reduction in Generalized One-Sided Formal Contexts. Information Sciences, 2017, 378: 317-327.
[128] 王振,魏玲.基于单边区间集概念格的不完备形式背景的属性约简.计算机科学, 2018, 45(1): 73-78.
(WANG Z, WEI L. Attribute Reduction of Partially-Known Formal Concept Lattices for Incomplete Contexts. Computer Science, 2018, 45(1): 73-78.)
[129] 王振.基于部分已知概念格的不完备形式背景的属性约简与规则提取.硕士学位论文.西安:西北大学, 2018.
(WANG Z. Attribute Reduction and Rule Acquisition of Incomplete Formal Contexts Based on Partially-Known Concept Lattices. Master Dissertation. Xi′an, China: Northwest University, 2018.)
[130] LIU M, SHAO M W, ZHANG W X, et al. Reduction Method for Concept Lattices Based on Rough Set Theory and Its Application. Computers and Mathematics with Applications, 2007, 53(9): 1390-1410.
[131] QIN K Y, LI B, PEI Z. Attribute Reduction and Rule Acquisition of Formal Decision Context Based on Object (Property) Oriented Concept Lattices. International Journal of Machine Learning and Cybernetics, 2019, 10(10): 2837-2850.
[132] ZOU L, PANG K, SONG X Y, et al. A Knowledge Reduction Approach for Linguistic Concept Formal Context. Information Sciences, 2020, 524: 165-183.
[133] CORNEJO M E, MEDINA J, RAMIREZ-POUSSA E. Attribute and Size Reduction Mechanisms in Multi-Adjoint Concept La-ttices. Journal of Computational and Applied Mathematics, 2017, 318: 388-402.
[134] REN R S, WEI L. The Attribute Reductions of Three-Way Concept Lattices. Knowledge-Based Systems, 2016, 99: 92-102.
[135] QI J J, QIAN T, WEI L. The Connections between Three-Way and Classical Lattices. Knowledge-Based Systems, 2016, 91: 143-151.
[136] LI M Z, WANG G Y. Approximate Concept Construction with Three-Way Decisions and Attribute Reduction in Incomplete Contexts. Knowledge-Based Systems, 2016, 91: 165-178.
[137] 曹丽,魏玲,祁建军.保持二元关系不变的概念约简.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. Pattern Recognition and Artificial Intelligence, 2018, 31(6): 516-524.)
[138] KEPRT A, SNÁŠEL V. Binary Factor Analysis with Help of Formal Concepts // Proc of the International Workshop on Concept Lattices and Their Applications. Berlin, Germany: Springer, 2004: 90-101.
[139] BÉLOHLÁVEK R, VYCHODIL V. On Boolean Factor Analysis with Formal Concept as Factors // Proc of the International Conference on Soft Computing and Intelligent Systems and International Symposium on Advanced Intelligent Systems. Washington, USA: IEEE, 2006: 1054-1059.
[140] BÉLOHLÁVEK R, VYCHODIL V. Discovery of Optimal Factors in Binary Data via a Novel Method of Matrix Decomposition. Journal of Computer and System Sciences, 2010, 76(1): 3-20.
[141] BÉLOHLÁVEK R, TRNECKA M. From-below Approximations in Boolean Matrix Factorization: Geometry and New Algorithm. Journal of Computer and System Sciences, 2015, 81(8): 1678-1697.
[142] 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/OL]. [2019-09-06]. http://engine.scichina.com/publisher/scp/journal/SSI/doi/10.1360/N112018-00272?slug=abstract.
(WEI L, CAO L, QI J J, et al. Concept Reduction and Concept Characteristics in Formal Concept Analysis [J/OL]. [2019-09-06]. http://engine.scichina.com/publisher/scp/journal/SSI/doi/10.1360/N112018-00272?slug=abstract.)
[143] 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.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. Journal of Shandong University(Natural Science), 2020, 55(5): 32-45.)
[144] MAIER D. The Theory of Relational Data Bases. Rockville, USA: Computer Science Press, 1983.
[145] AGRAWAL R, SRIKANT R. Fast Algorithms for Mining Association Rules // Proc of the 20th International Conference on Very Large Data Bases. San Francisco, USA: Morgan Kaufmann Publishers, 1994: 487-499.
[146] MISSAOUI R, GODIN R. Search for Concepts and Dependencies in Databases // ZIARKO W P, ed. Rough Sets, Fuzzy Sets and Knowledge Discovery. Berlin, Germany: Springer, 1994: 16-23.
[147] 王志海,胡可云,胡学钢,等.概念格上规则提取的一般算法与渐进式算法.计算机学报, 1999, 22(1): 66-70.
(WANG Z H, HU K Y, HU X G, et al. General and Incremental Algorithms of Rule Extraction Based on Concept Lattice. Chinese Journal of Computers, 1999, 22(1): 66-70.)
[148] 谢志鹏,刘宗田.概念格与关联规则发现.计算机研究与发展, 2000, 37(12): 1415-1421.
(XIE Z P, LIU Z T. Concept Lattice and Association Rule Discovery. Journal of Computer Research and Development, 2000, 37(12): 1415-1421.)
[149] 胡可云,陆玉昌,石纯一.基于概念格的分类和关联规则的集成挖掘方法.软件学报, 2000, 11(11): 1478-1484.
(HU K Y, LU Y C, SHI C Y. An Integrated Mining Approach for Classification and Association Rule Based on Concept Lattice. Journal of Software, 2000, 11(11): 1478-1484.)
[150] 梁吉业,王俊红.基于概念格的规则产生集挖掘算法.计算机研究与发展, 2004, 41(8): 1339-1344.
(LIANG J Y, WANG J H. An Algorithm for Extracting Rule-Generating Sets Based on Concept Lattice. Journal of Computer Research and Development, 2004, 41(8): 1339-1344.)
[151] SAHAMI M. Learning Classification Rules Using Lattices // Proc of the European Conference on Machine Learning. Berlin, Germany: Springer, 1995: 343-346.
[152] DUQUENNE V, GUIGUES J L. Famille Minimale d′Implications Informatives Résultant d′un Tableau de Données Binaires. Mathématiques et Sciences Humaines, 1986, 24(95): 5-18.
[153] SERTKAYA B. Towards the Complexity of Recognizing Pseudo-Intents // Proc of the 17th International Conference on Conceptual Structures. Berlin, Germany: Springer, 2009: 284-292.
[154] BABIN M A, KUZNETSOV S O. Recognizing Pseudo-Intents Is coNP-Complete // Proc of the 7th International Conference on Concept Lattices and Their Applications. Berlin, Germany: Springer, 2010: 294-301.
[155] QU K S, ZHAI Y H. Generating Complete Set of Implications for Formal Contexts. Knowledge-Based Systems, 2008, 21(5): 429-433.
[156] 马垣,张学东,迟呈英.紧致依赖与内涵亏值.软件学报, 2011, 22(5): 962-972.
(MA Y, ZHANG X D, CHI C Y. Compact Dependencies and Intent Waned Values. Journal of Software, 2011, 22(5): 962-971.)
[157] ZAKI M J, OGIHARA M. Theoretical Foundations of Association Rules // Proc of the 3rd ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery. New York, USA: ACM, 1998: 1-8.
[158] BASTIDE Y, PASQUIER N, TAOUIL R, et al. Mining Minimal Non-redundant Association Rules Using Frequent Closed Itemsets // Proc of the 1st International Conference on Computational Lo-gic. Berlin, Germany: Springer, 2000: 972-986.
[159] BALCAZAR J L. Redundancy, Deduction Schemes, and Minimum-Size Bases for Association Rules. Logical Methods in Computer Science, 2010, 6(2): 1-33.
[160] BELOHLAVEK R, DE BAETS B, OUTRATA J, et al. Inducing Decision Trees via Concept Lattices. International Journal of General Systems, 2009, 38(4): 455-467.
[161] QU K S, ZHAI Y H, ZHAO Y M, et al. Study of Decision Implications Based on Formal Concept Analysis. Journal of Systems Science and Information, 2006, 4(3): 533-542.
[162] STUMME G, TAOUIL R, BASTIDE Y, et al. Fast Computation of Concept Lattices Using Data Mining Techniques // Proc of the 7th International Workshop on Knowledge Representation Meets Databases. Berlin, Germany: Springer, 2000: 129-139.
[163] LI J H, MEI C L, KUMAR C A, et al. On Rule Acquisition in Decision Formal Contexts. International Journal of Machine Learning and Cybernetics, 2013, 4(6): 721-731.
[164] LI J H, HUANG C C, MEI C L, et al. An Intensive Study on Rule Acquisition in Formal Decision Contexts Based on Minimal Closed Label Concept Lattices. Intelligent Automation and Soft Computing, 2017, 23(3): 519-533.
[165] ZHANG S X, LI D Y, ZHAI Y H, et al. A Comparative Study of Decision Implication, Concept Rule and Granular Rule. Information Sciences, 2020, 508: 33-49.[166] WEI L, LIU L, QI J J, et al. Rules Acquisition of Formal Decision Contexts Based on Three-Way Concept Lattices. Information Sciences, 2020, 516: 529-544.
[167] ZHAI Y H, LI D Y, QU K S. Decision Implications: A Logical Point of View. International Journal of Machine Learning and Cybernetics, 2014, 5(4): 509-516.
[168] ZHAI Y H, LI D Y, QU K S. Decision Implication Canonical Basis: A Logical Perspective. Journal of Computer and System Sciences, 2015, 81(1): 208-218.
[169] 翟岩慧,李德玉,曲开社.决策蕴涵规范基.电子学报, 2015, 43(1): 18-23.
(ZHAI Y H, LI D Y, QU K S. Canonical Basis for Decision Implications. Acta Electronica Sinica, 2015, 43(1): 18-23.)
[170] LI D Y, ZHANG S X, ZHAI Y H. Method for Generating Decision Implication Canonical Basis Based on True Premises. International Journal of Machine Learning and Cybernetics, 2017, 8(1): 57-67.
[171] ZHAI Y H, LI D Y, ZHANG J. Variable Decision Knowledge Representation: A Logical Description. Journal of Computational Science, 2017, 25: 161-169.
[172] ZHAI Y H, LI D Y, QU K S. Fuzzy Decision Implications. Knowledge-Based System, 2013, 37: 230-236.
[173] ZHAI Y H, LI D Y, QU K S. Fuzzy Decision Implication Canonical Basis. International Journal of Machine Learning and Cybernetics, 2018, 9(11): 1909-1917.
[174] ZHAI Y H, LI D Y, QU K S. Probability Fuzzy Attribute Implications for Interval-Valued Fuzzy Sets. International Journal of Database Theory and Application, 2012, 5(4): 95-108.
[175] BÉLOHLÁVEK R, VYCHODIL V. Attribute Implications in a Fu-zzy Setting // Proc of the 4th International Conference on Formal Concept Analysis. Berlin, Germany: Springer, 2006: 45-60.
[176] LI J H, HUANG C C, QI J J, et al. Three-Way Cognitive Concept Learning via Multi-granularity. Information Sciences, 2017, 378: 244-263.
[177] 米允龙,李金海,刘文奇,等.MapReduce框架下的粒概念认知学习系统研究.电子学报, 2018, 46(2): 289-297.
(MI Y L, LI J H, LIU W Q, et al. Research on Granular Concept Cognitive Learning System under MapReduce Framework. Acta Electronica Sinica, 2018, 46(2): 289-297.)
[178] NIU J J, HUANG C C, LI J H, et al. Parallel Computing Techniques for Concept-Cognitive Learning Based on Granular Computing. International Journal of Machine Learning and Cybernetics, 2018, 9(11): 1785-1805.
[179] HUANG C C, LI J H, MEI C L, et al. Three-Way Concept Learning Based on Cognitive Operators: An Information Fusion Viewpoint. International Journal of Approximate Reasoning, 2017, 83: 218-242.
[180] LI J H, HUANG C C, XU W H, et al. Cognitive Concept Lear-ning via Granular Computing for Big Data // Proc of the International Conference on Machine Learning and Cybernetics. Wa-shington, USA: IEEE, 2015: 289-294.
[181] 李金海,米允龙,刘文奇.概念的渐进式认知理论与方法.计算机学报, 2019, 42(10): 2233-2250.
(LI J H, MI Y L, LIU W Q. Incremental Cognition of Concepts: Theories and Methods. Chinese Journal of Computers, 2019, 42(10): 2233-2250.)
[182] 李金海,吴伟志,邓硕.形式概念分析的多粒度标记理论.山东大学学报(理学版), 2019, 54(2): 30-40.
(LI J H, WU W Z, DENG S. Multi-scale Theory in Formal Concept Analysis. Journal of Shandong University(Natural Science), 2019, 54(2): 30-40.)
[183] 李金海,李玉斐,米允龙,等.多粒度形式概念分析的介粒度标记方法.计算机研究与发展, 2020, 57(2): 447-458.
(LI J H, LI Y F, MI Y L, et al. Meso-Granularity Labeled Method for Multi-granularity Formal Concept Analysis. Journal of Computer Research and Development, 2020, 57(2): 447-458.)
[184] 李金海,贺建君,吴伟志.多粒度形式概念分析的类属性块优化.山东大学学报(理学版), 2020, 55(5): 1-12.
(LI J H, HE J J, WU W Z. Optimization of Class-Attribute Block in Multi-granularity Formal Concept Analysis. Journal of Shandong University(Natural Science), 2020, 55(5): 1-12.)
[185] BELOHLAVEK R, DE BAETS B, KONECNY J. Granularity of Attributes in Formal Concept Analysis. Information Sciences, 2014, 260: 149-170.
[186] SHE Y H, HE X L, QIAN T, et al. A Theoretical Study on Object-Oriented and Property-Oriented Multi-scale Formal Concept Analysis. International Journal of Machine Learning and Cybernetics, 2019, 10(11): 3263-3271.
[187] SHAO M W, LÜ M M, LI K W, et al. The Construction of Attribute(Object)-Oriented Multi-granularity Concept Lattices. International Journal of Machine Learning and Cybernetics, 2020, 11(5): 1017-1032.
[188] XIE J P, YANG M H, LI J H, et al. Rule Acquisition and Optimal Scale Selection in Multi-scale Formal Decision Contexts and Their Applications to Smart City. Future Generation Computer Systems, 2018, 83: 564-581.
[189] 郝晨,范敏,李金海,等.多标记背景下基于粒标记规则的最优标记选择.模式识别与人工智能, 2016, 29(3): 272-280.
(HAO C, FAN M, LI J H, et al. Optimal Scale Selection in Multi-scale Contexts Based on Granular Scale Rules. Pattern Re-cognition and Artificial Intelligence, 2016, 29(3): 272-280.)
[190] LI J H, LIU Z M. Granule Description in Knowledge Granularity and Representation. Knowledge-Based Systems, 2020, 203: 106160.
[191] YAO Y Y. Rough-Set Concept Analysis: Interpreting RS-Definable Concepts Based on Ideas from Formal Concept Analysis. Information Sciences, 2016, 346/347: 442-462.
[192] 智慧来,李金海.基于必然属性分析的粒描述.计算机学报, 2018, 41(12): 2702-2719.
(ZHI H L, LI J H. Granule Description Based on Necessary Attribute Analysis. Chinese Journal of Computers, 2018, 41(12): 2702-2719.)
[193] ZHI H L, LI J H. Granule Description Based on Positive and Negative Attributes. Granular Computing, 2019, 4(3): 337-350.
[194] ZHI H L, LI J H. Granule Description Based Knowledge Disco-very from Incomplete Formal Contexts via Necessary Attribute Analysis. Information Sciences, 2019, 485: 347-361.
[195] WAN Q, LI J H, WEI L, et al. Optimal Granule Level Selection: A Granule Description Accuracy Viewpoint. International Journal of Approximate Reasoning, 2020, 116: 85-105.
[196] STUMME G, MAEDCHE A. FCA-MERGE: Bottom-up Merging of Ontologies // Proc of the 17th International Joint Conference on Artificial Intelligence. San Francisco, USA: Morgan Kaufmann Publishers, 2001: 225-230.
[197] CHEN R C, BAU C T, YEH C J. Merging Domain Ontologies Based on the Wordnet System and Fuzzy Formal Concept Analysis Techniques. Applied Soft Computing, 2011, 11(2): 1908-1923.
[198] ZHAO Y, WANG X, HALANG W. Ontology Mapping Based on Rough Formal Concept Analysis[C/OL]. [2020-04-07]. https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1602
313.
[199] ZHAO M Y, ZHANG S M, LI W Z, et al. Matching Biomedical Ontologies Based on Formal Concept Analysis. Journal of Biomedical Semantics, 2018, 9. DOI: 10.1186/s13326-018-0178-9.
[200] 朱佳,王向前,张宝隆,等.基于形式概念分析的煤矿事故本体构建.工矿自动化, 2018, 44(5): 26-30.
(ZHU J, WANG X Q, ZHANG B L, et al. Construction of Coal Mine Accident Ontology Based on Formal Concept Analysis. Industry and Mine Automation, 2018, 44(5): 26-30.)
[201] 金阳,左万利.多维概念格与多维序列模式的增量挖掘.计算机研究与发展, 2007, 44(11): 1816-1824.
(JIN Y, ZUO W L. Multi-dimensional Concept Lattice and Incremental Discovery of Multi-dimensional Sequential Patterns. Journal of Computer Research and Development, 2007, 44(11): 1816-1824.)
[202] 刘馨蕊,张伟峰.基于多维多值概念格的矿山生产地学本体构建研究.地球信息科学学报, 2018, 20(2): 176-185.
(LIU X R, ZHANG W F. Construction of Mine Production Geo-Ontology Based on Multi-dimensional and Many-Valued Concept Lattices. Journal of Geo-information Science, 2018, 20(2): 176-185.)
[203] 渠寒花,惠建忠,何险峰,等.气象服务形式概念分析模型研究.计算机工程与应用, 2018, 54(9): 257-264.
(QU H H, HUI J Z, HE X F, et al. Formal Concept Analysis Model of Meteorological Services. Computer Engineering and Applications, 2018, 54(9): 257-264.)
[204] 覃丽珍,李金海,王扬扬.基于概念格的知识发现及其在高校就业数据分析中的应用.山东大学学报(理学版), 2015, 50(12): 58-64.
(QIN L Z, LI J H, WANG Y Y. Concept Lattice Based Know-ledge Discovery and Its Application to Analysis of Employment Data in Universities. Journal of Shandong University(Natural Science), 2015, 50(12): 58-64.)
[205] 张涛,李慧,任宏雷.博客数据的属性拓扑分析.燕山大学学报, 2015, 39(1): 42-50.
(ZHANG T, LI H, REN H L. Attribute Topology Analysis of Blogger Data. Journal of Yanshan University, 2015, 39(1): 42-50.)
[206] AGON C, ANDREATTA M, ATIF J, et al. Musical Descriptions Based on Formal Concept Analysis and Mathematical Morphology // Proc of the International Conference on Conceptual Structures. Berlin, Germany: Springer, 2018: 105-119.
[207] ZHANG T, LIU M Q, LIU W Y. The Causality Research between Syndrome Elements by Attribute Topology. Computational and Mathematical Methods in Medicine, 2018. DOI: 10.1155/2018/9707581.
[208] 王慧,秦静,郑涛.量化概念格上网络盗窃行为拟合预测.中国人民公安大学学报(自然科学版), 2017, 23(2): 63-67.
(WANG H, QIN J, ZHENG T. Fitting Prediction of Network Theft on Quantitative Concept Lattice. Journal of People′s Public Security University of China(Science and Technology), 2017, 23(2): 63-67.)
[209] CASTELLANOS A, CIGARRÁN J, GARCIA-SERRANO A. Formal Concept Analysis for Topic Detection: A Clustering Quality Experimental Analysis. Information Systems, 2017, 66: 24-42.
[210] HAO S F, SHI C Y, NIU Z D, et al. Concept Coupling Learning for Improving Concept Lattice-Based Document Retrieval. Engineering Applications of Artificial Intelligence, 2018, 69: 65-75.
[211] ZHANG T, LI H H, LIU M Q, et al. Incremental Concept-Cognitive Learning Based on Attribute Topology. International Journal of Approximate Reasoning, 2020, 118: 173-189.
[212] 王凯,杨枢,刘玉文.基于多层次概念格的图像场景语义分类方法.山西师范大学学报(自然科学版), 2017, 31(2): 27-34.
(WANG K, YANG S, LIU Y W. A Semantic Classification Method of Image Scene Based on Concept Lattice Hierarchy. Journal of Shanxi Normal University(Natural Science Edition), 2017, 31(2): 27-34.)
[213] 王亚平,张素兰,张继福,等.基于模糊概念格的视觉单词生成方法.小型微型计算机系统, 2016, 37(8): 1868-1872.
(WANG Y P, ZHANG S L, ZHANG J F, et al. Visual Words Generation Method Based on the Fuzzy Concept Lattice. Journal of Chinese Computer Systems, 2016, 37(8): 1868-1872.)
[214] YAO Y Y. Interpreting Concept Learning in Cognitive Informatics and Granular Computing. IEEE Transactions on Systems, Man, and Cybernetics(Cybernetics), 2009, 39(4): 855-866.
[215] WANG Y X. On Concept Algebra: A Denotational Mathematical Structure for Knowledge and Software Modelling. International Journal of Cognitive Informatics and Natural Intelligence, 2008, 2(2): 1-19.
[216] KUMAR C A, ISHWARYA M S, LOO C K. Formal Concept Analysis Approach to Cognitive Functionalities of Bidirectional Associative Memory. Biologically Inspired Cognitive Architectures, 2015, 12: 20-33.
[217] FAN B J, TSANG E C C, XU W H, et al. Attribute-Oriented Cognitive Concept Learning Strategy: A Multi-level Methods. International Journal of Machine Learning and Cybernetics, 2019, 10(9): 2421-2437.
[218] YAN E L, SONG J L, REN Y L, et al. Construction of Three-Way Attribute Partial Order Structure via Cognitive Science and Granular Computing. Knowledge-Based Systems, 2020, 197: 105859.
[219] 张文修,徐伟华.基于粒计算的认知模型.工程数学学报, 2007, 24(6): 957-971.
(ZHANG W X, XU W H. Cognitive Model Based on Granular Computing. Chinese Journal of Engineering Mathematics, 2007, 24(6): 957-971.)
[220] 张清华,周玉兰,腾海涛.基于粒计算的认知模型.重庆邮电大学学报(自然科学版), 2009, 21(4): 494-501.
(ZHANG Q H, ZHOU Y L, TENG H T. Cognition Model Based on Granular Computing. Journal of Chongqing University of Posts and Telecommunications(Natural Science Edition), 2009, 21(4): 494-501.)
[221] CHEN J K, MI J S, LIN Y J. A Graph Approach for Knowledge Reduction in Formal Contexts. Knowledge-Based Systems, 2018, 148: 177-188.
[222] MAO H, MIAO H R. Attribute Reduction Based on Directed Graph in Formal Fuzzy Contexts. Journal of Intelligent and Fuzzy Systems, 2018, 34(6): 4139-4148.
[223] GUO L K, LI Q G, ZHANG G Q. A Representation of Continuous Domains via Relationally Approximable Concepts in a Gene-ralized Framework of Formal Concept Analysis. International Journal of Approximate Reasoning, 2019, 114: 29-43.
[224] LANG G M, LUO J F, YAO Y Y. Three-Way Conflict Analysis: A Unification of Models Based on Rough Sets and Formal Concept Analysis. Knowledge-Based Systems, 2020, 194. DOI: 10.101
6/j.knosys.2020.105556.
[225] 徐伟华,李金海,魏玲,等.形式概念分析理论与应用.北京:科学出版社, 2016.
(XU W H, LI J H, WEI L, et al. Formal Concept Analysis: Theory and Application. Beijing, China: Science Press, 2016.)
[226] POELMANS J, IGNATOV D I, KUZNETSOV S O, et al. Formal Concept Analysis in Knowledge Processing: A Survey on Applications. Expert Systems with Applications, 2013, 40(16): 6538-6560.
[227] MA J M, ZHANG W X. Axiomatic Characterizations of Dual Concept Lattices. International Journal of Approximate Reasoning, 2013, 54(5): 690-697.
[228] SONG X X, WANG X, ZHANG W X. Independence of Axiom Sets Characterizing Formal Concepts. International Journal of Machine Learning and Cybernetics, 2013, 4(5): 459-468.
[229] 张慧雯,刘文奇,李金海.不完备形式背景下近似概念格的公理化方法.计算机科学, 2015, 42(6): 67-70, 92.
(ZHANG H W, LIU W Q, LI J H. Axiomatic Characterizations of Approximate Concept Lattices in Incomplete Contexts. Compu-ter Science, 2015, 42(6): 67-70, 92.)
[230] 陈锦坤,李进金.概念格的公理化.计算机工程与应用, 2012, 48(5): 41-43.
(CHEN J K, LI J J. Axiomatization of Concept Lattice. Computer Engineering and Applications, 2012, 48(5): 41-43.)
[231] SHAO M W, WU W Z, WANG C Z. Axiomatic Characterizations of Adjoint Generalized(Dual) Concept Systems. Journal of Intelligent and Fuzzy Systems, 2019, 37(3): 3629-3638.
[232] POELMANS J, KUZNETSOV S O, IGNATOV D I, et al. Formal Concept Analysis in Knowledge Processing: A Survey on Models and Techniques. Expert Systems with Applications, 2013, 40(16): 6601-6623.
[233] POELMANS J, IGNATOV D I, KUZNETSOV S O, et al. Fuzzy and Rough Formal Concept Analysis: A Survey. International Journal of General Systems, 2014, 43(2): 105-134.
[234] REN R S, WEI L, YAO Y Y. An Analysis of Three Types of Partially-Known Formal Concepts. International Journal of Machine Learning and Cybernetics, 2018, 9(11): 1767-1783.
[235] 仇国芳,张志霞,张炜.基于粗糙集方法的概念格理论研究综述.模糊系统与数学, 2014, 28(1): 168-177.
(QIU G F, ZHANG Z X, ZHANG W. A Survey for Study on Concept Lattice Theory via Rough Set. Fuzzy Systems and Mathematics, 2014, 28(1): 168-177.)
[236] YANG H Z, LEUNG Y, SHAO M W. Rule Acquisition and Attribute Reduction in Real Decision Formal Contexts. Soft Computing, 2011, 15(6): 1115-1128.
[237] JANOSTIK R, KONECNY J. General Framework for Consistencies in Decision Contexts. Information Sciences, 2020, 530: 180-200.
[238] ZHANG Z, DU J, WANG L M. Formal Concept Analysis App-roach for Data Extraction from a Limited Deep Web Database. Journal of Intelligent Information Systems, 2013, 41(2): 211-234.
[239] XU J, WANG G Y, LI T R, et al. Local-Density-Based Optimal Granulation and Manifold Information Granule Description. IEEE Transactions on Cybernetics, 2018, 48(10): 2795-2808.
[240] ZHU X B, PEDRYCZ W, LI Z W. Granular Data Description: Designing Ellipsoidal Information Granules. IEEE Transactions on Cybernetics, 2017, 47(12): 4475-4484.
[241] KUZNETSOV S O. Machine Learning on the Basis of Formal Concept Analysis. Automation and Remote Control, 2001, 62(10): 1543-1564.
[242] IGNATOV D I, GNATYSHAK D V, KUZNETSOV S O, et al. Triadic Formal Concept Analysis and Triclustering: Searching for Optimal Patterns. Machine Learning, 2015, 101(1/2/3): 271-302.
[243] 于剑.图灵测试的明与暗.计算机研究与发展, 2020, 57(5): 906-911.
(YU J. Brilliance and Darkness: Turing Test. Journal of Computer Research and Development, 2020, 57(5): 906-911.)
[244] 李金海,闫梦宇,徐伟华,等.概念认知学习的若干问题与思考.西北大学学报(自然科学版), 2020, 50(4): 501-515.
(LI J H, YAN M Y, XU W H, et al. Some Problems and Thoughts in Concept-Cognitive Learning. Journal of Northwest University(Natural Science Edition), 2020, 50(4): 501-515.)