Analysis and Comparison of Concept Lattices from the Perspective of Three-Way Decisions
LI Leijun1,2, LI Meizheng3, XIE Bin4, MI Jusheng1,2
1.College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024. 2.Hebei Key Laboratory of Computational Mathematics and Applications, Hebei Normal University, Shijiazhuang 050024. 3.School of Information Science and Technology, Southwest Jiaotong University, Chengdu 610031. 4.College of Information Technology, Hebei Normal University, Shijiazhuang 050024
Abstract：Based on the construction of formal concepts and the constitution of formal contexts, the inherent connections between different concept lattices are explored from the perspective of three-way decisions. The comparison of the concept lattices in classical formal context and incomplete formal context, as well as in fuzzy formal context and intuitionistic fuzzy formal context, is given, respectively. Then, the important value of three-way decisions in concept lattice theory is shown. Compared with the concept lattices in classical formal context and fuzzy formal context, the concept lattices in incomplete formal context and intuitionistic fuzzy formal context can reflect the idea of three-way decisions, and they have advantages of small data storage requirement, concise attribute reduction, etc.
李磊军，李美争，解滨，米据生. 三支决策视角下概念格的分析和比较*[J]. 模式识别与人工智能, 2016, 29(10): 951-960.
LI Leijun, LI Meizheng, XIE Bin, MI Jusheng. Analysis and Comparison of Concept Lattices from the Perspective of Three-Way Decisions. , 2016, 29(10): 951-960.
[1] WILLE R. Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts // Proc of the 7th International Conference on Formal Concept Analysis. Berlin, Germany: Springer, 2009: 314-339. [2] PRISS U. Formal Concept Analysis in Information Science. Annual Review of Information Science and Technology, 2006, 40(1): 521-543. [3] 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. [4] TILLEY T, EKLUND P. Citation Analysis Using Formal Concept Analysis: A Case Study in Software Engineering // Proc of the 18th International Workshop on Database and Expert Systems Applications. Washington, USA: IEEE, 2007: 545-550. [5] POELMANS J, IGNATOV D I, VIAENE S, et al. Text Mining Scientific Papers: A Survey on FCA-Based Information Retrieval Research // Proc of the 12th Industrial Conference on Advances in Data Mining: Applications and Theoretical Aspects. Berlin, Germany: Springer, 2012: 273-287. [6] LAKHAL L, STUMME G. Efficient Mining of Association Rules Based on Formal Concept Analysis // GANTER B, STUMME G, WILLE R, eds. Formal Concept Analysis. Berlin, Germany: Springer, 2005: 180-195. [7] 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-Gene-rating Sets Based on Concept Lattice. Journal of Computer Research and Development, 2004, 41(8): 1339-1344.) [8] GANTER B, WILLE R. Formal Concept Analysis: Mathematical Foundations. Berlin, Germany: Springer, 1999. [9] YAO Y Y. An Outline of a Theory of Three-Way Decisions // Proc of the 8th International Conference on Rough Sets and Current Trends in Computing. Berlin, Germany: Springer, 2012: 1-17. [10] QI J J, WEI L, YAO Y Y. Three-Way Formal Concept Analysis // Proc of the 9th International Conference on Rough Sets and Knowledge Technology. Berlin, Germany: Springer, 2014: 732-741. [11] QI J J, QIAN T, WEI L. The Connections between Three-Way and Classical Concept Lattices. Knowledge-Based Systems, 2016, 91: 143-151. [12] REN R S, WEI L. The Attribute Reductions of Three-Way Concept Lattices. Knowledge-Based Systems, 2016, 99: 92-102. [13] 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. [14] LI J H, MEI C L, L Y J. Incomplete Decision Contexts: Appro-ximate Concept Construction, Rule Acquisition and Knowledge Reduction. International Journal of Approximate Reasoning, 2013, 54(1): 149-165. [15] RODRIGUEZ-JIMNEZ J M, CORDERO P, ENCISO M, et al. Negative Attributes and Implications in Formal Concept Analysis. Procedia Computer Science, 2014, 31: 758-765. [16] 刘 盾,李天瑞,苗夺谦,等.三支决策与粒计算.北京:科学出版社, 2013. (LIU D, LI T R, MIAO D Q, et al. Three-Way Decisions and Granular Computing. Beijing, China: Science Press, 2013.) [17] BURMEISTER P, HOLZER R. On the Treatment of Incomplete Knowledge in Formal Concept Analysis // Proc of the 8th International Conference on Conceptual Structures: Logical, Linguistic, and Computational Issues. Berlin, Germany: Springer, 2000: 385-398. [18] 智慧来.不完备形式背景上的知识表示.计算机科学, 2015, 42(1): 276-278. (ZHI H L. Knowledge Representation on Incomplete Formal Context. Computer Science, 2015, 42(1): 276-278.) [19] 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. Computer Science, 2015, 42(6): 67-70, 92.) [20] DAVEY B A, PRIESTLEY H A. Introduction to Lattices and Order. Cambridge, UK: Cambridge University Press, 1990. [21] PANG J Z, ZHANG X Y, XU W H. Attribute Reduction in In-tuitionistic Fuzzy Concept Lattices. Abstract and Applied Analysis, 2013. DOI: 10.1155/2013/271398. [22] KRAJCˇI S. Cluster Based Efficient Generation of Fuzzy Concepts. Neural Network World, 2003, 5: 521-530. [23] YAHIA S B, JAOUA A. Discovering Knowledge from Fuzzy Concept Lattice // KANDEL A, LAST M, BUNKE H, eds. Data Mi-ning and Computational Intelligence. Berlin, Germany: Springer, 2001: 167-190.
2016, Vol. 29 
