Skip to main content
SpringerLink
Log in

Local attribute reductions of formal contexts

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

Attribute reductions is an important topic in formal concept analysis. The existing attribute reduction approaches are dominated by global reductions and there is very limited investigation on local reductions. This paper is devoted to the study of decision rule specific reduction for formal decision context and concept specific reduction for formal context. The notion of decision rule specific reduction is proposed and the related reduction methods are presented. The relationships between existing reduction approaches and decision rule specific reduction approaches are analyzed. Accordingly, we make an analysis of attributes based on three-way classification by using reductions. Furthermore, the notion of concept specific reduction for formal context is proposed and the concept specific reduction methods are examined. The relationship between concept specific reduction and decision rule specific reduction is surveyed.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Belohlavek R, Vychodil V (2006) Formal concept analysis with constraints by closure operators. LNAI 4068:131–143

    MATH  Google Scholar 

  2. Beydoun G (2009) Formal concept analysis for an e-learning semantic web. Expert Syst Appl 36(8):10952–10961

    Google Scholar 

  3. Carpineto C, Romano G (2004) Exploiting the potential of concept lattices for information retrieval with CREDO. J UCS 10(8):985–1013

    MATH  Google Scholar 

  4. Chen DG, Tsang EC (2005) On the local reduction of information system. LNCS 3930:588–594

    Google Scholar 

  5. Chen DG, Zhao SY (2010) Local reduction of decision system with fuzzy rough sets. Fuzzy Sets Syst 161:1871–1883

    MathSciNet  MATH  Google Scholar 

  6. Dias SM, Vieira NJ (2015) Concept lattices reduction: definition, analysis and classification. Expert Syst Appl 42:7084–7097

    Google Scholar 

  7. Elloumi S, Jaam J, Hasnah A, Jaoua A, Nafkha I (2004) A multi-level conceptual data reduction approach based on the lukasiewicz implication. Inf Sci 163:253–262

    MathSciNet  MATH  Google Scholar 

  8. Formica A (2010) Concept similarity in fuzzy formal concept analysis for semantic web. Int J Uncertain Fuzz Knowl Based Syst 18(2):153–167

    MathSciNet  Google Scholar 

  9. Formica A (2012) Semantic web search based on rough sets and fuzzy formal concept analysis. Knowl Based Syst 26:40–47

    Google Scholar 

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

    MATH  Google Scholar 

  11. Klimes J (2014) Using formal concept analysis for control in cyber-physical systems. Proced Eng 69:1518–1522

    Google Scholar 

  12. Konecny J (2017) On attribute reduction in concept lattices: methods based on discernibility matrix are outperformed by basic clarification and reduction. Inf Sci 415:199–212

    Google Scholar 

  13. Kuznetsov SO (2001) Machine learning on the basis of formal concept analysis. Autom Rem Control 62(10):1543–1564

    MATH  Google Scholar 

  14. Kuznetsov SO (2004) Complexity of learning in concept lattices from positive and negative examples. Discret Appl Math 142:111–125

    MathSciNet  MATH  Google Scholar 

  15. Li JH, Mei CL, Lv YJ (2011) Knowledge reduction in decision formal contexts. Knowl Based Syst 24:709–715

    MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  17. Li JH, Mei CL, Lv YJ (2012) Knowledge reduction in formal decision contexts based on an order-preserving mapping. Int J Gener Syst 41:143–161

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  19. Li JH, Huang C, Mei CL, Yin YQ (2017) An intensive study on rule acquisition in formal decision contexts based on minimal closed label concept lattices. Intell Autom Soft Comput 23:519–533

    Google Scholar 

  20. Li JH, Kumar CA, Mei CL, Wang XZ (2017) Comparison of reduction in formal decision contexts. Int J Approx Reason 80:100–122

    MathSciNet  MATH  Google Scholar 

  21. Li JY, Wang X, Wu WZ, Xu YH (2017) Attribute reduction in inconsistent formal decision contexts based on congruence relations. Int J Mach Learn Cybern 8:81–94

    Google Scholar 

  22. Liu GL, Hua Z, Zhou JY (2018) Local attribute reductions for decision tables. Inf Sci 422:204–217

    MathSciNet  Google Scholar 

  23. Outrata J, Vychodil V (2012) Fast algorithm for computing fixpoints of Galois connections induced by object-attribute relational data. Inf Sci 185:114–127

    MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  25. Pei D, Mi JS (2011) Attribute reduction in decision formal context based on homomorphism. Int J Mach Learn Cybern 2:289–293

    Google Scholar 

  26. Pineda-Bautista BB, Carrasco-Ochoa JA, Martinez-Trinidad JF (2011) General framework for class-specific feature selection. Expert Syst Appl 38:10018–10024

    Google Scholar 

  27. Poelmans J, Elzinga P, Viaene S, Dedene G (2010) Formal concept analysis in knowledge discovery: a survey. In: International conference on conceptual structures, pp 139–153

    Google Scholar 

  28. Ren RS, Wei L (2016) The attribute reductions of three-way concept lattices. Knowl Based Syst 99:92–102

    Google Scholar 

  29. Sampath S, Sprenkle S, Gibson E, Pollock L, Greenwald AS (2007) Applying concept analysis to user-session-based testing of web applications. IEEE Trans Softw Eng 33(10):643–658

    Google Scholar 

  30. Shao MW, Li KW (2017) Attribute reduction in generalized one-sided formal contexts. Inf Sci 378:317–327

    MathSciNet  Google Scholar 

  31. Shao MW, Leung Y, Wu WZ (2014) Rule acquisition and complexity reduction in formal decision contexts. Int J Approx Reason 55:259–274

    MathSciNet  MATH  Google Scholar 

  32. Shao MW, Yang HZ, Wu WZ (2015) Knowledge reduction in formal fuzzy contexts. Knowl Based Syst 73:265–275

    Google Scholar 

  33. Skowron A, Rauszer C (1992) The discernibility matrices and functions in information systems. In: Slowinski R (ed) Intelligent decision support, handbook of applications and advances of the rough sets theory. Kluwer Academic, Dordrecht, pp 331–362

    Google Scholar 

  34. Wei L, Qi JJ (2010) Relation between concept lattice reduction and rough set reduction. Knowl Based Syst 23:934–938

    Google Scholar 

  35. Wei L, Qi J, Zhang W (2008) Attribute reduction theory of concept lattice based on decision formal contexts. Sci China Ser F Inf Sci 51(7):910–923

    MathSciNet  MATH  Google Scholar 

  36. Wille R (1982) Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival I (ed) Ordered sets. Springer, Dordrecht, pp 445–470

    Google Scholar 

  37. Wu WZ, Leung Y, Mi JS (2009) Granular computing and knowledge reduction in formal contexts. IEEE Trans Knowl Data Eng 21(10):1461–1474

    Google Scholar 

  38. Yao Y (2004) A comparative study of formal concept analysis and rough set theory in data analysis. In: International conference on rough sets and current trends in computing, Springer, pp 59–68

  39. Yao Y, Zhang XY (2017) Class-specific attribute reducts in rough set theory. Inf Sci 418:601–618

    Google Scholar 

  40. Zhang ML, Wu L (2015) LIFT: multi-label learning with label-specific features. IEEE Trans Pat Ana and Mach Intell 37:107–120

    Google Scholar 

  41. Zhang WX, Qiu GF (2005) Uncertain decision making based on rough sets. Publishin of Tsinghua University, Beijing

    Google Scholar 

  42. Zhang W, Wei L, Qi J (2005) Attribute reduction theory and approach to concept lattice. Sci China Ser F Inf Sci 48(6):713–726

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work has been partially supported by the National Natural Science Foundation of China (Grant nos. 61473239, 61372187).

Author information

Authors and Affiliations

  1. School of Mathematics, Southwest Jiaotong University, Chengdu, 610031, Sichuan, China

    Keyun Qin, Hong Lin & Yuting Jiang

Authors
  1. Keyun Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hong Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuting Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hong Lin.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qin, K., Lin, H. & Jiang, Y. Local attribute reductions of formal contexts. Int. J. Mach. Learn. & Cyber. 11, 81–93 (2020). https://doi.org/10.1007/s13042-019-00956-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-019-00956-z

Keywords

Search

Navigation