A Layer-by-Layer Attribute Reduction Algorithm for Fuzzy Linguistic Attribute Partial Order Structure Diagram
PANG Kuo1, ZHOU Ai1, YANG Xinran2, LI Nan2, ZOU Li3, LU Mingyu1
1. Information Science and Technology College, Dalian Maritime University, Dalian 116026; 2. School of Computer and Information Technology, Liaoning Normal University, Dalian 116081; 3. School of Computer Science and Technology, Shandong Jianzhu University, Jinan 250102
Abstract：As a data visualization tool, attribute partial order structure diagram can solve the problem of user cognitive overload in formal concept analysis effectively. People often express preference information through fuzzy linguistic values in real life,and thus a large amount of fuzzy linguistic-valued data is generated. To solve the problem of attribute reduction in fuzzy linguistic environment, a layer-by-layer attribute reduction algorithm for fuzzy linguistic attribute partial order structure diagram is proposed in this paper. Firstly, the fuzzy linguistic attribute partial order structure diagram is constructed based on the fuzzy linguistic-valued formal context, and the fuzzy linguistic-valued data is embedded into the attribute partial order structure diagram. The order relation and the incomparable relation between fuzzy linguistic values are expressed by the linguistic truth-valued lattice implication algebra acting as the representation model of the fuzzy linguistic values. Secondly, the fuzzy linguistic attribute partial order structure diagram is employed and the nodes that do not form edges with the underlying nodes are searched to obtain the minimum attribute subset with the fuzzy linguistic-valued formal context discrimination ability unchanged. On the premise of ensuring the class equivalence of the fuzzy linguistic attribute partial order structure diagram, the difference attribute between the node and its child nodes is calculated, and the corresponding layer-by-layer attribute reduction model is constructed. Finally, examples and comparative experiments verify the effectiveness and practicability of the proposed method.
庞阔, 周爱, 杨鑫冉, 李楠, 邹丽, 鲁明羽. 模糊语言属性偏序结构图的逐层属性约简算法[J]. 模式识别与人工智能, 2022, 35(9): 774-788.
PANG Kuo, ZHOU Ai, YANG Xinran, LI Nan, ZOU Li, LU Mingyu. A Layer-by-Layer Attribute Reduction Algorithm for Fuzzy Linguistic Attribute Partial Order Structure Diagram. Pattern Recognition and Artificial Intelligence, 2022, 35(9): 774-788.
[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] MI Y L, LIU W Q, SHI Y, et al. Semi-Supervised Concept Lear-ning by Concept-Cognitive Learning and Concept Space. IEEE Transactions on Knowledge and Data Engineering, 2020, 34(5): 2429-2442. [3] MI Y L, SHI Y, LI J H, et al. Fuzzy-Based Concept Learning Method: Exploiting Data with Fuzzy Conceptual Clustering. IEEE Transactions on Cybernetics, 2022, 52(1): 582-593. [4] KUZNETSOV S O, MAKHAZHANOV N, USHAKOV M.On Neural Network Architecture Based on Concept Lattices // Proc of the International Symposium on Methodologies for Intelligent Systems. Berlin, Germany: Springer, 2017: 653-663. [5] 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. [6] LAN N, YANG S Q, YIN L, et al. Research on Knowledge Graphs with Concept Lattice Constraints. Symmetry, 2021, 13(12). DOI: 10.3390/sym13122363. [7] 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. [8] MUANGPRATHUB J, BOONJING V, CHAMNONGTHAI K.Lear-ning Recommendation with Formal Concept Analysis for Intelligent Tutoring System. Heliyon, 2020, 6(10). DOI: 10.1016/j.heliyon.2020.e05227. [9] MEZNI H, ABDELJAOUED T.A Cloud Services Recommendation System Based on Fuzzy Formal Concept Analysis. Data and Know-ledge Engineering, 2018, 116: 100-123. [10] MEDINA J, NAVAREÑO P, RAMÍREZ-POUSSA E. Knowledge Implications in Multi-adjoint Concept Lattices // Proc of the 11th European Symposium on Computational Intelligence and Mathema-tics. Berlin, Germany: Springer, 2022: 155-161. [11] ZOU L, KANG N, CHE L, et al. Linguistic-Valued Layered Concept Lattice and Its Rule Extraction. International Journal of Machine Learning and Cybernetics, 2022, 13(1): 83-98. [12] SINGH P K.Bipolar δ-Equal Complex Fuzzy Concept Lattice with Its Application. Neural Computing and Applications, 2020, 32(7): 2405-2422. [13] ZOU L, PANG K, SONG X Y, et al. A Knowledge Reduction Approach for Linguistic Concept Formal Context. Information Sciences, 2020, 524: 165-183. [14] CUI H, YUE G L, ZOU L, et al. Multiple Multidimensional Linguistic Reasoning Algorithm Based on Property-Oriented Linguistic Concept Lattice. International Journal of Approximate Reasoning, 2021, 131: 80-92. [15] PEI Z, RUAN D, LIU J, et al. Linguistic Values Based Intelligent Information Processing: Theory, Methods, and Applications. Berlin, Germany: Springer, 2010. [16] HONG W X, LI S X, YU J P, et al. A New Approach of Generation of Structural Partial-Ordered Attribute Diagram. ICIC Express Letters(Applications), 2012, 3(4): 823-830. [17] HONG W X, MAO J Y, YU J P, et al. The Complete Definitions of Attributes and Abstract Description of Attribute Features of the Formal Context. ICIC Express Letters, 2013, 7(3): 997-1003. [18] LUAN J M, HONG W X, LIU J M, et al. The Complete Definitions of Object and Abstract Description of Object Features of the Formal Context. ICIC Express Letters(Applications), 2013, 4(4): 1065-1072. [19] MENG H, HONG W X, YU C G, et al. Symptom-Herb Know-ledge Discovery Based on Attribute Partial Ordered Structure Diagrams. Granular Computing, 2021, 6(2): 229-240. [20] MENG H, HAN X Y.Knowledge Discovery for Spleen Yang Deficiency Syndrome Based on Attribute Partial Order Structure Diagram. International Journal of Computer Applications in Technology, 2020, 64(1): 92-99. [21] ZHENG C F.A Novel Classification Tree Based on Local Minimum Gini Index and Attribute Partial Order Structure Diagram. Interna-tional Journal of Computer Applications in Technology, 2020, 64(1): 33-45. [22] YU J P, LI C, HONG W X, et al. A New Approach of Rules Extraction for Word Sense Disambiguation by Features of Attributes. Applied Soft Computing, 2015, 27: 411-419. [23] ZADEH L A.Fuzzy Logic = Computing with Words. IEEE Transactions on Fuzzy Systems, 1996, 4(2): 103-111. [24] ZUHEROS C, LI C C, CABRERIZO F J, et al. Computing with Words: Revisiting the Qualitative Scale. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2018, 26(S2): 127-143. [25] LI C C, DONG Y C, HERRERA F, et al. Personalized Individual Semantics in Computing with Words for Supporting Linguistic Group Decision Making: An Application on Consensus Reaching. Information Fusion, 2017, 33: 29-40. [26] MENDEL J M.On Computing the Similarity of Trapezoidal Fuzzy Sets Using an Automated Area Method. Information Sciences, 2022, 589: 716-737. [27] GONG J W, LIU H C, YOU X Y, et al. An Integrated Multi-criteria Decision Making Approach with Linguistic Hesitant Fuzzy Sets for E-Learning Website Evaluation and Selection. Applied Soft Computing, 2021, 102. DOI: 10.1016/j.asoc.2021.107118. [28] ROMERO Á L, RODRÍGUEZ R M, MARTÍNEZ L. Computing with Comparative Linguistic Expressions and Symbolic Translation for Decision Making: ELICIT Information. IEEE Transactions on Fuzzy Systems, 2020, 28(10): 2510-2522. [29] GOU X J, XU Z S, LIAO H C, et al. Probabilistic Double Hierarchy Linguistic Term Set and Its Use in Designing an Improved VIKOR Method: The Application in Smart Healthcare. Journal of the Operational Research Society, 2021, 72(12): 2611-2630. [30] XU Y, CHEN S W, MA J.Linguistic Truth-Valued Lattice Implication Algebra and Its Properties // Proc of the Multiconference on Computational Engineering in Systems Application. Washington, USA: IEEE, 2006: 1413-1418. [31] ZOU L, LIN H M, SONG X Y, et al. Rule Extraction Based on Linguistic-Valued Intuitionistic Fuzzy Layered Concept Lattice. International Journal of Approximate Reasoning, 2021, 133: 1-16. [32] 李金海,魏玲,张卓,等.概念格理论与方法及其研究展望.模式识别与人工智能, 2020, 33(7) : 619-642. (LI J H, WEI L, ZHANG Z, et al. Concept Lattice Theory and Method and Their Research Prospect. Pattern Recognition and Artificial Intelligence, 2020, 33(7): 619-642.) [33] 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 Method of Concept Lattice. Science in China(Information Sciences), 2005, 35(6): 628-639.) [34] WEI L, QI J J.Relation between Concept Lattice Reduction and Rough Set Reduction. Knowledge-Based Systems, 2010, 23(8): 934-938. [35] DIAS S M, VIEIRA N J.A Methodology for Analysis of Concept Lattice Reduction. Information Sciences, 2017, 396: 202-217. [36] MAO H.Representing Attribute Reduction and Concepts in Con-cept Lattice Using Graphs. Soft Computing, 2017, 21(24): 7293-7311. [37] LI L J, LI M Z, MI J S, et al. A Simple Discernibility Matrix for Attribute Reduction in Formal Concept Analysis Based on Granular Concepts. Journal of Intelligent and Fuzzy Systems, 2019, 37(3): 4325-4337. [38] 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. [39] KONECNY J, KRAJ<inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="Mml194-1003-6059-35-9-774"><mml:mover><mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mrow><mml:mi>ˇ</mml:mi></mml:mrow></mml:mover></mml:math></inline-formula>A P. On Attribute Reduction in Concept La-ttices: The Polynomial Time Discernibility Matrix-Based Method Becomes the CR-Method. Information Sciences, 2019, 491: 48-62. [40] WANG Z, WEI L, QI J J, et al. Attribute Reduction of SE-ISI Concept Lattices for Incomplete Contexts. Soft Computing, 2020, 24(20): 15143-15158. [41] LIN Y D, LI J J, TAN A H, et al. Granular Matrix-Based Know-ledge Reductions of Formal Fuzzy Contexts. International Journal of Machine Learning and Cybernetics, 2020, 11(3): 643-656. [42] YAO Y Y, ZHAO Y.Discernibility Matrix Simplification for Constructing Attribute Reducts. Information Sciences, 2009, 179(7): 867-882. [43] SHAO M W, LÜ M M, LI K W,et al. The Construction of Attri-bute(Object)-Oriented Multi-granularity Concept Lattices. Inter-national Journal of Machine Learning and Cybernetics, 2020, 11(5): 1017-1032. [44] CHUNDURI R K, CHERUKURI A K.Scalable Formal Concept Analysis Algorithms for Large Datasets Using Spark. Journal of Ambient Intelligence and Humanized Computing, 2019, 10(11): 4283-4303. [45] ZOU L G, HE T T, DAI J H.A New Parallel Algorithm for Computing Formal Concepts Based on Two Parallel Stages. Information Sciences, 2022, 586: 514-524.
2022, Vol. 35 
