Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
research-article

An efficient method of renewing object-induced three-way concept lattices involving decreasing attribute-granularity levels

Published: 27 February 2024 Publication History
  • Get Citation Alerts
  • Abstract

    In three-way concept analysis, changing (decreasing or increasing) attribute-granularity levels is needed to seek desirable information. Reconstructing three-way concept lattices often requires huge computation and long elapsed time when attribute-granularity levels are changed. To avoid this problem, a good strategy is indirectly renewing three-way concept lattices. Our paper studies how to renew object-induced three-way concept lattices involving decreasing attribute-granularity levels. Firstly, we analyze changes of object-induced three-way concept lattices when attribute-granularity levels are decreased. To classify changes of object-induced three-way concepts, we classify these concepts into six categories, derive sufficient and necessary conditions of identifying these categories, and investigate their properties. To explore changes of covering relations among object-induced three-way concepts, we classify covering relations into three categories, and identify them by finding which are the destructors of deleted object-induced three-way concepts before the decrease, and analyzing which are children concepts of object-induced three-way concepts as destructors after the decrease. Secondly, by using the above analysis results, we put forward a novel algorithm called OEL-Collapse to renew object-induced three-way concept lattices when attribute-granularity levels are decreased. Finally, experiments are conducted to illustrate the efficiency of the OEL-Collapse algorithm.

    References

    [1]
    R. Wille, Restructuring lattice theory: an approach based on hierarchies of concepts, in: I. Rival (Ed.), Ordered Sets, Reidel, Dordrecht-Boston, 1982, pp. 445–470.
    [2]
    B. Ganter, R. Wille, Formal Concept Analysis: Mathematical Foundations, Springer, New York, 1999.
    [3]
    K. Siminski, Neuro-rough-fuzzy approach for regression modelling from missing data, Int. J. Appl. Math. Comput. Sci. 22 (2) (2012) 461–476.
    [4]
    J.H. Li, C.L. Mei, Y.J. Lv, Incomplete decision contexts: approximate concept construction, rule acquisition and knowledge reduction, Int. J. Approx. Reason. 54 (1) (2013) 149–165.
    [5]
    W.X. Zhang, G.F. Qiu, Uncertain Decision Making Based on Rough Sets, Tsinghua University Press, Beijing, China, 2005.
    [6]
    L. Ma, J.S. Mi, B. Xie, Multi-scaled concept lattices based on neighborhood systems, Int. J. Mach. Learn. Cybern. 8 (1) (2017) 149–157.
    [7]
    W.Z. Wu, Y. Leung, Optimal scale selection for multi-scale decision tables, Int. J. Approx. Reason. 54 (8) (2013) 1107–1129.
    [8]
    Y.Q. Tang, M. Fan, J.H. Li, An information fusion technology for triadic decision contexts, Int. J. Mach. Learn. Cybern. 7 (1) (2016) 13–24.
    [9]
    Z. Zhang, Constructing L-fuzzy concept lattices without fuzzy Galois closure operation, Fuzzy Sets Syst. 333 (2018) 71–86.
    [10]
    K. Pang, P.S. Liu, S.X. Li, L. Zou, M.Y. Lu, L. Martínez, Concept lattice simplification with fuzzy linguistic information based on three-way clustering, Int. J. Approx. Reason. 154 (2023) 149–175.
    [11]
    C. Alcalde, A. Burusco, H. Bustince, M. Sesma-Sara, Trend analysis in L-fuzzy contexts with absent values, Iran. J. Fuzzy Syst. 17 (3) (2020) 69–84.
    [12]
    P.K. Singh, Processing linked formal fuzzy contexts using non-commutative composition, Inst. Integr. Omics Appl. Biotechn. 7 (5) (2016) 21–32.
    [13]
    L.G. Zou, Z.P. Zhang, J. Long, A fast incremental algorithm for constructing concept lattices, Expert Syst. Appl. 42 (9) (2015) 4474–4481.
    [14]
    R. Belohlavek, B. De Baets, J. Konecny, Granularity of attributes in formal concept analysis, Inf. Sci. 260 (2014) 149–170.
    [15]
    L.G. Zou, Z.P. Zhang, J. Long, An efficient algorithm for increasing the granularity levels of attributes in formal concept analysis, Expert Syst. Appl. 46 (2016) 224–235.
    [16]
    Z.Y. Hu, M.W. Shao, M.S. Liang, Rule acquisition in generalized one-sided decision systems, Lect. Notes Comput. Sci. 13633 (2022) 176–190.
    [17]
    L. Wei, L. Liu, J.J. Qi, T. Qian, Rules acquisition of formal decision contexts based on three-way concept lattices, Inf. Sci. 516 (2020) 529–544.
    [18]
    M.W. Shao, Y. Leung, Relations between granular reduct and dominance reduct in formal contexts, Knowl.-Based Syst. 65 (1) (2014) 1–11.
    [19]
    S.Y. Zhao, J.J. Qi, J.A. Li, L. Wei, Concept reduction in formal concept analysis based on representative concept matrix, Int. J. Mach. Learn. Cybern. 14 (4) (2023) 1147–1160.
    [20]
    J.H. Li, W.H. Xu, Y.H. Qian, Concept learning via granular computing: a cognitive viewpoint, Inf. Sci. 298 (2015) 447–467.
    [21]
    J.H. Li, C.C. Huang, J.J. Qi, Y.H. Qian, W.Q. Liu, Three-way cognitive concept learning via multi-granularity, Inf. Sci. 378 (2017) 244–263.
    [22]
    W.H. Xu, D.D. Guo, Y.H. Qian, W.P. Ding, Two-way concept-cognitive learning method: a fuzzy-based progressive learning, IEEE Trans. Fuzzy Syst. 31 (6) (2023) 1885–1899.
    [23]
    J.J. Qi, L. Wei, Y.Y. Yao, Three-way formal concept analysis, Lect. Notes Comput. Sci. 8818 (2014) 732–741.
    [24]
    J.J. Qi, T. Qian, L. Wei, The connections between three-way and classical concept lattices, Knowl.-Based Syst. 91 (2016) 143–151.
    [25]
    P.K. Singh, Three-way fuzzy concept lattice representation using neutrosophic set, Int. J. Mach. Learn. Cybern. 8 (1) (2017) 69–79.
    [26]
    R.S. Ren, L. Wei, The attribute reductions of three-way concept lattices, Knowl.-Based Syst. 99 (2016) 92–102.
    [27]
    H.Y. Yu, Q.G. Li, M.J. Cai, Characteristics of three-way concept lattices and three-way rough concept lattices, Knowl.-Based Syst. 146 (2018) 181–189.
    [28]
    T. Qian, L. Wei, J.J. Qi, A theoretical study on the object (property) oriented concept lattices based on three-way decisions, Soft Comput. 23 (19) (2019) 9477–9489.
    [29]
    T.Q. Deng, B.H. Long, W.H. Xu, Y.Y. Yao, Adjunctive three-way concepts from positive and negative concepts in lattice-valued formal contexts, Int. J. Approx. Reason. 161 (2023).
    [30]
    M.W. Shao, Z.Y. Hu, W.Z. Wu, H. Liu, Graph neural networks induced by concept lattices for classification, Int. J. Approx. Reason. 154 (2023) 262–276.
    [31]
    S. Kuznetsov, Machine learning and formal concept analysis, Lect. Notes Comput. Sci. 2961 (2004) 287–312.
    [32]
    Y.Y. Yao, Three-way decisions with probabilistic rough sets, Inf. Sci. 180 (3) (2010) 341–353.
    [33]
    Y.Y. Yao, Three-way decision and granular computing, Int. J. Approx. Reason. 103 (2018) 107–123.
    [34]
    A. Shah, N. Azam, B. Ali, M.T. Khan, J.T. Yao, A three-way clustering approach for novelty detection, Inf. Sci. 569 (2021) 650–668.
    [35]
    H. Yu, L.Y. Chen, J.T. Yao, A three-way density peak clustering method based on evidence theory, Knowl.-Based Syst. 211 (2021).
    [36]
    D. Liu, The effectiveness of three-way classification with interpretable perspective, Inf. Sci. 567 (2021) 237–255.
    [37]
    X. Yang, Y.J. Li, Q.K. Li, D. Liu, T.R. Li, Temporal-spatial three-way granular computing for dynamic text sentiment classification, Inf. Sci. 596 (2022) 551–566.
    [38]
    G.M. Lang, D.Q. Miao, H. Fujita, Three-way group conflict analysis based on Pythagorean fuzzy set theory, IEEE Trans. Fuzzy Syst. 28 (3) (2020) 447–461.
    [39]
    J.F. Luo, M.J. Hu, G.M. Lang, X. Yang, K.Y. Qin, Three-way conflict analysis based on alliance and conflict functions, Inf. Sci. 594 (2022) 322–359.
    [40]
    F. Hao, Y.X. Yang, G.Y. Min, V. Loia, Incremental construction of three-way concept lattice for knowledge discovery in social networks, Inf. Sci. 578 (2021) 257–280.
    [41]
    D.C. Liang, Y.Y. Fu, Z.S. Xu, Three-way group consensus decision based on hierarchical social network consisting of decision makers and participants, Inf. Sci. 585 (2022) 289–312.
    [42]
    J. Zhou, W. Pedrycz, C. Gao, H.L. Zhi, X.D. Yue, Principles for constructing three-way approximations of fuzzy sets: a comparative evaluation based on unsupervised learning, Fuzzy Sets Syst. 413 (2021) 74–98.
    [43]
    Y.Y. Yao, J.L. Yang, Granular rough sets and granular shadowed sets: three-way approximations in Pawlak approximation spaces, Int. J. Approx. Reason. 142 (2022) 231–247.
    [44]
    X.W. Xin, J.H. Song, Z.A. Xue, W.M. Peng, Intuitionistic fuzzy three-way formal concept analysis based attribute correlation degree, J. Intell. Fuzzy Syst. 40 (1) (2021) 1567–1583.
    [45]
    X.L. He, L. Wei, Y.H. She, L-fuzzy concept analysis for three-way decisions: basic definitions and fuzzy inference mechanisms, Int. J. Mach. Learn. Cybern. 9 (11) (2018) 1857–1867.
    [46]
    X. Zhao, D. Miao, Isomorphic relationship between L-three-way concept lattices, Cogn. Comput. 14 (6) (2022) 1997–2019.
    [47]
    Y.Y. Yao, Interval sets and three-way concept analysis in incomplete contexts, Int. J. Mach. Learn. Cybern. 8 (1) (2017) 3–20.
    [48]
    R.S. Ren, L. Wei, Y.Y. Yao, An analysis of three types of partially-known formal concepts, Int. J. Mach. Learn. Cybern. 9 (11) (2018) 1767–1783.
    [49]
    H.L. Zhi, J.J. Qi, Common-possible concept analysis: a granule description viewpoint, Appl. Intell. 52 (3) (2022) 2975–2986.
    [50]
    J.J. Qi, L. Wei, R.S. Ren, 3-way concept analysis based on 3-valued formal contexts, Cogn. Comput. 14 (6) (2022) 1900–1912.
    [51]
    H.L. Zhi, J.J. Qi, T. Qian, L. Wei, Three-way dual concept analysis, Int. J. Approx. Reason. 114 (2019) 151–165.
    [52]
    C.C. Huang, J.H. Li, C.L. Mei, W.Z. Wu, Three-way concept learning based on cognitive operators: an information fusion viewpoint, Int. J. Approx. Reason. 83 (2017) 218–242.
    [53]
    H.L. Zhi, J.J. Qi, T. Qian, R.S. Ren, Conflict analysis under one-vote veto based on approximate three-way concept lattice, Inf. Sci. 516 (2020) 316–330.
    [54]
    P.K. Singh, Medical diagnoses using three-way fuzzy concept lattice and their Euclidean distance, Comput. Appl. Math. 37 (3) (2018) 3283–3306.
    [55]
    T. Qian, L. Wei, J.J. Qi, Constructing three-way concept lattices based on apposition and subposition of formal contexts, Knowl.-Based Syst. 116 (2017) 39–48.
    [56]
    W.W. Wang, J.J. Qi, Algorithm for constructing three-way concepts, J. Xidian Univ. 44 (1) (2017) 71–76.
    [57]
    S.C. Yang, Y.N. Lu, X.Y. Jia, W.W. Li, Constructing three-way concept lattice based on the composite of classical lattices, Int. J. Approx. Reason. 121 (2020) 174–186.
    [58]
    B.H. Long, W.H. Xu, X.Y. Zhang, L. Yang, The dynamic update method of attribute-induced three-way granular concept in formal contexts, Int. J. Approx. Reason. 126 (2020) 228–248.
    [59]
    Q. Hu, K.Y. Qin, L. Yang, The updating methods of object-induced three-way concept in dynamic formal contexts, Appl. Intell. 53 (2) (2022) 1826–1841.
    [60]
    Q. Hu, K.Y. Qin, L. Yang, A constructing approach to multi-granularity object-induced three-way concept lattices, Int. J. Approx. Reason. 150 (2022) 229–241.
    [61]
    Bache, K.; Lichman, M. (2013): UCI machine learning repository. http://archive.ics.uci.edu/ml.
    [62]
    J. Alcalá-Fdez, A. Fernandez, J. Luengo, J. Derrac, S. García, L. Sánchez, F. Herrera, KEEL data-mining software tool: data set repository, integration of algorithms and experimental analysis framework, J. Mult.-Valued Log. Soft Comput. 17 (2-3) (2011) 255–287.

    Index Terms

    1. An efficient method of renewing object-induced three-way concept lattices involving decreasing attribute-granularity levels
          Index terms have been assigned to the content through auto-classification.

          Recommendations

          Comments

          Information & Contributors

          Information

          Published In

          cover image International Journal of Approximate Reasoning
          International Journal of Approximate Reasoning  Volume 164, Issue C
          Jan 2024
          381 pages

          Publisher

          Elsevier Science Inc.

          United States

          Publication History

          Published: 27 February 2024

          Author Tags

          1. Three-way concept analysis
          2. Object-induced three-way concept lattice
          3. Conceptual knowledge updating
          4. Attribute-granularity level

          Qualifiers

          • Research-article

          Contributors

          Other Metrics

          Bibliometrics & Citations

          Bibliometrics

          Article Metrics

          • 0
            Total Citations
          • 0
            Total Downloads
          • Downloads (Last 12 months)0
          • Downloads (Last 6 weeks)0

          Other Metrics

          Citations

          View Options

          View options

          Get Access

          Login options

          Media

          Figures

          Other

          Tables

          Share

          Share

          Share this Publication link

          Share on social media