Skip to main content
Log in

Abstract

Formal concept analysis is an effective tool for data analysis and knowledge discovery. Corresponding to concept lattice in a formal context, object-oriented concept lattice is introduced based on rough set. Obtaining object-oriented concepts is important but difficult because of the higher time complexity. In order to solve this question, we first divide the power set of the attribute set into the layered sets in this paper. Since for any object-oriented concept, the object-oriented concept extension and object-oriented concept intension determine each other uniquely, we introduce the layered extension sets. By discussing the properties of layered extension sets, the approach to acquire object-oriented concepts is investigated, and related concept acquirement algorithm is also depicted. Examples prove that the concept acquirement approach is valid.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Alcalde C, Burusco A, Fuentes-González R, Zubia I (2009) Treatment of L-fuzzy contexts with absent values. Info Sci 179:1–15

    Article  MathSciNet  MATH  Google Scholar 

  2. Ashfaq RAR, Wang XZ, Huang JZX, Abbas H, He YL (2016) Fuzziness based semi-supervised learning approach for intrusion detection system. Info Sci. doi:10.1016/j.ins.2016.04.019

  3. B\(\check{e}\)lohl\(\acute{a}\)vek R, Sklen\(\acute{a}\check{r}\) V, Zacpal J, (2005) Crisply generated fuzzy concepts. In: Ganter B, Godin R (eds) LNAI, 3403. Springer-Verlag, Berlin/Heideberg, pp 268–283

  4. Burusco a, Fuentes-Gonzales R (1994) The study of the L-fuzzy concept lattice. Mathware Soft Computing 1(3):209–218

    MathSciNet  MATH  Google Scholar 

  5. Burusco A, Fuentes-Gonzales R (1998) Construction of the L-fuzzy concept lattice. Fuzzy Sets Syst 97(1):109–114

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen YH, Yao YY (2008) A multiview approach for intelligent data analysis based on data operators. Info Sci 178:1–20

    Article  MathSciNet  MATH  Google Scholar 

  7. Chaudron L, Maille N (2000) Generalized formal concept analysis. In: The 8th International Conference on Conceptual Structures, Springer, Berlin, vol 1867, pp.357–370

  8. D\(\ddot{u}\)ntsch I, Gediga G, (2003) Approximation operators in qualitative data analysis. Theory and Application of Relational Structures as Knowledge Instruments, Springer, Heidelberg, pp 216–233

  9. D\(\ddot{u}\)ntsch I, Gediga G (2002) Modal-style operators in qualitative data analysis. In: Proceeding of 2002 IEEE International Conference on Data Mining, pp. 155–162

  10. Ganter B, Wille R (1999) Formal concept analysis: mathe matical foundations. Springer, Berlin

    Book  MATH  Google Scholar 

  11. He YL, Liu JNK, Hu YH, Wang XZ. OWA operator based link prediction ensemble for social network. Expert Syst Appl 42(1):21–50

  12. He YL, Wang XZ, Huang JZX (2016) Fuzzy nonlinear regression analysis using a random weight network. Info Sci 364–365:222–240

    Article  Google Scholar 

  13. Hu KY, Sui YF, Lu YC, Wang J, Shi CY (2001) Concept approximation in concept lattices. In: Advance in knowledge discovery and data mining, Proceeding of 5th Pacific-Asia Conference, Springer, Berlin, Vol 2035, pp. 167–173

  14. Jaoua A, Elloumi S (2001) Galois connection, formal concept and Galois lattice in real binary relation. J Syst Software 60:149–163

    Article  Google Scholar 

  15. Kent RE (1996) Rough concept analysis: a synthesis of rough sets and formal concept analysis. Fundamenta Info 27:169–181

    MathSciNet  MATH  Google Scholar 

  16. Kaytoue M, Kuznetsov SO, Napoli A, Duplessis S (2011) Mining gene expression data with pattern structures in formal concept analysis. Info Sci 181:1989–2001

    Article  MathSciNet  Google Scholar 

  17. Krajci S (2003) Cluster based efficient generation of fuzzy concepts. Neural Network World 5:521–530

    Google Scholar 

  18. Lai HL, Zhang DX (2009) Concept lattices of fuzzy contexts: Formal concept analysis vs. rough set theory. Int J Approximate Reasoning 50(5):695–707

    Article  MathSciNet  MATH  Google Scholar 

  19. Latiri CC, Elloumi S, Chevallet JP, Jaoua A (2003) Extension of fuzzy Galois connection for information retrieval using a fuzzy quantifier. In: ACS/IEEE International Conference on Computer Systems and Applications, Tunis, Tunisia

  20. Li JH, Mei CL, Lv YJ (2012) Knowledge reduction in real decision formal contexts. Info Sci 189:191–207

    Article  MathSciNet  MATH  Google Scholar 

  21. Li JH, Mei CL, Lv YJ (2013) Incomplete decision contexts: approximate concept construction, rule acquisition and knowledge reduction. Int J Approximate Reasoning 54(1):149–165

    Article  MathSciNet  MATH  Google Scholar 

  22. Li JH, Mei CL, Wang JH, Zhang X (2014) Rule-preserved object compression in formal decision contexts using concept lattices. Knowledge-Based Syst 71:435–445

    Article  Google Scholar 

  23. Li JH, Mei CL, Xu WH, Qian YH (2015) Concept learning via granular computing: a cognitive viewpoint. Info Sci 298(1):447–467

    Article  MathSciNet  Google Scholar 

  24. Li JH, Ren Y, Mei CL, Qian YH, Yang XB (2016) A comparative study of multigranulation rough sets and concept lattices via rule acquisition. Knowledge-Based Syst 91:152–164

    Article  Google Scholar 

  25. Li JH, Huang CC, Qi JJ, Qian YH, Liu WQ (2016) Three-way cognitive concept learning via multi-granularity. Info Sci. doi:10.1016/j.ins.2016.04.051

  26. Li LF, Zhang JK (2010) Attribute reduction in fuzzy concept lattices based on the \(T\) implication. Knowledge-Based Syst 23:497–503

    Article  Google Scholar 

  27. Li MZ, Wang GY (2016) Approximate concept construction with three-way decisions and attribute reduction in incomplete contexts. Knowledge-Based Syst 91:165–178

    Article  Google Scholar 

  28. Ma JM, Zhang WX, Cai S (2006) Variable threshold concept lattice and dependence space. Int Conf Nat Comput Int Conf Fuzzy Syst Knowledge Discovery 4223:109–128

    Google Scholar 

  29. Ma JM, Zhang WX, Wang X (2006) Dependence space of concept lattices based on rough set. In: Proceedings of the 2006 IEEE International Conference on Granular Computing, pp. 200–204

  30. Ma JM (2007) The mathematical characterizations of some models on rough set and concept lattice. PhD Dissertation, Xi’an Jiaotong University, September

  31. Ma JM (2009) Concept granular computing system. Sixth Int Conf Fuzzy Systems Knowledge Discovery 1:150–154

    Google Scholar 

  32. Ma JM, Leung Y, Zhang WX (2014) Attribute reductions in object-oriented concept lattices. Int J Machine Learning Cybernerics 5(5):789–813

    Article  Google Scholar 

  33. Pawlak Z (1981) Information systems-theoretical foundations. Info Syst 6:205–218

    Article  MATH  Google Scholar 

  34. Pawlak Z (1982) Rough sets. Int J Comput Info Sci 11:341–356

    Article  MathSciNet  MATH  Google Scholar 

  35. Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data. Kluwer Academic Publishers, Dordrecht, Boston, London

    Book  MATH  Google Scholar 

  36. Qi JJ, Qian T, Wei L (2016) The connections between three-way and classical concept lattices. Knowledge-Based Syst 91:143–151

    Article  Google Scholar 

  37. Qian T, Wei L (2014) A novel concept acquisition approach based on formal contexts. Sci World J 2014:1–7

    Article  Google Scholar 

  38. Qiu GF (2007) Learning models based on formal context. Lecture Notes Artificial Intelligence Springer Berlin 4481:419–426

    Google Scholar 

  39. Ren RS, Wei L (2016) The attribute reductions of three-way concept lattices. Knowledge-Based Syst 99:92–100

    Article  Google Scholar 

  40. Shao MW, Leung Y, Wu WZ (2014) Rule acquisition and complexity reduction in formal decision contexts. Int J Approximate Reasoning 55(1):259–274

    Article  MathSciNet  MATH  Google Scholar 

  41. Tadrat J, Boonjing V, Pattaraintakorn P (2012) A new similarity measure in formal concept analysis for case-based reasoning. Expert Syst Appl 39:967–972

    Article  Google Scholar 

  42. Wang LD, Liu XD (2008) Concept analysis via rough set and AFS algebra. Info Sci 178:4125–4137

    Article  MathSciNet  MATH  Google Scholar 

  43. Wang XZ, Xing HJ, Li Y, Hua Q, Dong CR, Pedrycz W (2015) A Study on relationship between generalization abilities and fuzziness of base classifiers in ensemble learning. IEEE Trans Fuzzy Syst 23(5):1638–1654

    Article  Google Scholar 

  44. Wang XZ (2015) Learning from big data with uncertainty-editorial. J Intell Fuzzy Syst 28(5):2329–2330

    Article  MathSciNet  Google Scholar 

  45. Wang XZ, Ashfaq RAR, Fu AM (2015) Fuzziness based sample categorization for classifier performance improvement. J Intell Fuzzy Syst 29(3):1185–1196

  46. Wille R (1982) Restructuring lattice theory: an approach based on hierarchies of concepts. Ordered Sets, Reidel, Dordrecht, pp 445–470

    MATH  Google Scholar 

  47. Wu WZ, Leung Y, Mi JS (2009) Granular computing and knowledge reduction in formal contexts. IEEE Transactions on Knowledge and Data. Engineering 21(10):1461–1474

    Google Scholar 

  48. Xu WH, Li WT (2016) Granular computing approach to two-way learning based on formal concept analysis in fuzzy datasets. IEEE Trans Cybernetics 46(2):366–377

    Article  Google Scholar 

  49. Yao YY (2004) Concept lattices in rough set theory. In: Proceeding of 2004 annual meeting of the north american fuzzy information processing society, pp. 796–801

  50. Yao YY (2004) A comparative study of formal concept analysis and rough set theory in data analysis. 4th International conference on rough sets and current trends in computing, LNCS 3066. Springer, Beilin, pp 59–68

    Google Scholar 

  51. Yao YY, Chen Y (2004) Rough set approximations in formal concept analysis. In: 2004 Annual meeting of the north american fuzzy information processing society, pp. 73–78

  52. Yao YY (2006) Rough set approximations: a concept analysis point of view. Transactions on Rough Sets V, LNCS 4100:285–305

    Article  MATH  Google Scholar 

  53. Yao YY (2012) An outline of a theory of three-way decisions. In: Procesdings of the 8th international conference on rough sets and current trends in computing (RSCTC 2012), LNCS (LNAI), vol 7413, pp 1–17

  54. Yao YY, Deng XF (2013) A granular computing paradigm for concept learning. In: Rammanna S, Jain L, Howlett RJ (eds) Emerging paradigms in machine learning. Springer, London, pp 307–326

    Chapter  Google Scholar 

  55. Yao YY (2016) Three-way decisions and cognitive computing. Cognitive Computation. doi:10.1007/s12559-016-9397-5

    Google Scholar 

  56. Zhang JF, Jiang YY, Chang KH, Zhang SL, Lai JH, Hu LH (2009) A concept lattice based outlier mining method in low-dimensional subspaces. Patt Recog Lett 30:1434–1439

    Article  Google Scholar 

  57. Zhang WX, Qiu GF (2003) Uncertain decision making based on rough sets. Tsinghua University Press, Beijing

    Google Scholar 

  58. Zhang WX, Wei L, Qi JJ (2005) Attribute reduction theory and approach to concept lattice. Sci China Ser F-Info Sci 48:713–726

    Article  MathSciNet  MATH  Google Scholar 

  59. Zhang WX, Ma JM, Fan SQ (2007) Variable threshold concept lattice. Info Sci 177:4883–4892

    Article  MathSciNet  MATH  Google Scholar 

  60. Zhao YX, Li JH, Liu WQ, Xu WH (2016) Cognitive concept learning from incomplete information. Int J Machine Learning Cybernetics. doi:10.1007/s13042-016-0553-8

Download references

Acknowledgments

This work was supported by a grant from the National Natural Science Foundation of China (No. 10901025).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jian-Min Ma.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ma, JM., Cai, MJ. & Zou, CJ. Concept acquisition approach of object-oriented concept lattices. Int. J. Mach. Learn. & Cyber. 8, 123–134 (2017). https://doi.org/10.1007/s13042-016-0576-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-016-0576-1

Keywords

Navigation