On rule acquisition in decision formal contexts | International Journal of Machine Learning and Cybernetics Skip to main content
Springer Nature Link
Log in

On rule acquisition in decision formal contexts

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

Abstract

Rule acquisition is one of the main purposes in the analysis of decision formal contexts. Up to now, there have existed several types of rules (e.g., the decision rules and the granular rules) in decision formal contexts. This study firstly proposes a new algorithm with less time complexity for deriving the non-redundant decision rules from a decision formal context. Then, we invesigate decision rules and the granular rules in the consistent decision formal contexts and make a contrast between the decision rule oriented knowledge reduction and the granular rule oriented knowledge reduction. Finally, some experiments are conducted to assess the efficiency of the proposed rule acquisition algorithm.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

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

  2. Zhang WX, Wei L, Qi JJ (2005) Attribute reduction theory and approach to concept lattice. Sci China Ser F 48(6):713–726

    Article  MathSciNet  MATH  Google Scholar 

  3. Liu M, Shao MW, Zhang WX, Wu C (2007) Reduction method for concept lattices based on rough set theory and its applications. Comput Math Appl 53(9):1390–1410

    Article  MathSciNet  MATH  Google Scholar 

  4. Wang X, Zhang WX (2008) Relations of attribute reduction between object and property oriented concept lattices. Knowl Based Syst 21:398–403

    Article  Google Scholar 

  5. Medina J (2012) Relating attribute reduction in formal, object-oriented and property-oriented concept lattices. Comput Math Appl 64(6):1992–2002

    Article  MathSciNet  MATH  Google Scholar 

  6. Li TJ, Wu WZ (2011) Attribute reduction in formal contexts: a covering rough set approach. Fund Inform 111:15–32

    MathSciNet  MATH  Google Scholar 

  7. Mi JS, Leung Y, Wu WZ (2010) Approaches to attribute reduction in concept lattices induced by axialities. Knowl Based Syst 23(6):504–511

    Article  Google Scholar 

  8. Wei L, Qi JJ (2010) Relation between concept lattice reduction and rough set reduction. Knowl Based Syst 23(8):934–938

    Article  Google Scholar 

  9. Cherukuri AK, Srinivas S (2010) Concept lattice reduction using fuzzy K-means clustering. Expert Syst Appl 37(3):2696–2704

    Article  Google Scholar 

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

    Book  MATH  Google Scholar 

  11. Guigues JL, Duquenne V (1986) Famille minimales d’implications informatives résultant d’un tableau de données binaries. Math Sci Hum 95:5–18

    MathSciNet  Google Scholar 

  12. Luxenburger M (1991) Implications partielles dans un contexte. Math Sci Hum 113:35–55

    MathSciNet  MATH  Google Scholar 

  13. Dodin R, Missaoui R (1994) An incremental concept formation approach for learning from databases. Theor Comput Sci 133:387–419

    Article  Google Scholar 

  14. Valtchev P, Missaoui R, Godin R (2004) Formal concept analysis for knowledge discovery and data mining: the new challenge. In: Proceedings of the 2004 international conference on formal concept analysis, Sydney, Australia, pp 352–371

  15. Qu KS, Zhai YH (2008) Generating complete set of implications for formal contexts. Knowl Based Syst 21:429–433

    Article  Google Scholar 

  16. Pasquier N, Bastide Y, Taouil R et al (1999) Efficient mining of association rules using closed itemset lattices. Inform Sci 24(1):25–46

    Google Scholar 

  17. Zaki MJ (2004) Mining non-redundant association rules. Data Min Knowl Disc 9:223–248

    Article  MathSciNet  Google Scholar 

  18. Cherukuri AK (2012) Fuzzy clustering based formal concept analysis for association rules mining. Appl Artif Intell 26(3):274–301

    Article  Google Scholar 

  19. Zhang WX, Qiu GF (2005) Uncertain decision making based on rough sets. Tsinghua University Press, Beijing

    Google Scholar 

  20. Qu KS, Zhai YH, Liang JY et al (2007) Study of decision implications based on formal concept analysis. Int J Gen Syst 36(2):147–156

    Article  MathSciNet  MATH  Google Scholar 

  21. Shao MW (2007) Knowledge acquisition in decision formal contexts. In: Proceedings of the sixth international conference on machine learning and cybernetics, Hong Kong, pp 4050–4054

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

    Article  Google Scholar 

  23. Li J, Mei C, Lv Y (2011) A heuristic knowledge-reduction method for decision formal contexts. Comput Math Appl 61(4):1096–1106

    Article  MathSciNet  MATH  Google Scholar 

  24. Li J, Mei C, Lv Y (2011) Knowledge reduction in decision formal contexts. Knowl Based Syst 24(5):709–715

    Article  Google Scholar 

  25. Li J, Mei C, Lv Y (2012) Knowledge reduction in formal decision contexts based on an order-preserving mapping. Int J Gen Syst 41(2):143–161

    Article  MathSciNet  MATH  Google Scholar 

  26. Song XX, Wang X, Zhang WX (2012) Independence of axiom sets characterizing formal concepts. Int J Mach Learn Cybern. doi:10.1007/s13042-012-0110-z

  27. Kent RE (1994) Rough concept analysis. In: Ziarko WP (ed) Rough sets, Fuzzy sets and knowledge discovery. Springer, London, pp 248–255

  28. Yao YY (2004) Concept lattices in rough set theory. In: Proceedings of 2004 annual meeting of the north American fuzzy information processing society, Banff, Canada, pp 796–801

  29. Düntsch I, Gediga G (2003) Approximation operators in qualitative data analysis. In: Swart H et al (eds) Theory and applications of relational structures as knowledge instruments, Lecture Notes in Computer Science, vol 2929. Springer, Berlin, pp 214–230

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

    Article  MathSciNet  Google Scholar 

  31. Pei D, Mi JS (2011) Attribute reduction in decision formal context based on homomorphism. Int J Mach Learn Cyber 2(4):289–293

    Article  Google Scholar 

  32. Wang H, Zhang WX (2008) Approaches to knowledge reduction in generalized consistent decision formal contexts. Math Comput Model 48:1677–1684

    Article  MATH  Google Scholar 

  33. Fielding AH (2007) Clustering and classification techniques for the biosciences. Cambridge University Press, London

    Google Scholar 

  34. Frank A, Asuncion A (2010) UCI machine learning repository [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science

  35. Pei D, Li MZ, Mi JS (2011) Attribute reduction in fuzzy decision formal contexts. In: International conference on machine learning and cybernetics. IEEE Press, New York, pp 204–208

  36. Li J, Mei C, Lv Y (2013) Incomplete decision contexts: approximate concept construction, rule acquisition and knowledge reduction. Int J Approx Reason 54(1):149–165

    Article  MathSciNet  MATH  Google Scholar 

  37. Li J, Mei C, Lv Y (2012) Knowledge reduction in real decision formal contexts. Inform Sci 189:191–207

    Article  MathSciNet  MATH  Google Scholar 

  38. Li J, Mei C, Lv Y, Zhang X (2012c) A heuristic knowledge reduction algorithm for real decision formal contexts. In: Yao JT et al (eds) Proceedings of RSCTC, Lecture Notes in Artificial Intelligence, vol 7413. Springer, Berlin, pp 303–312

  39. Yang HZ, Leung Y, Shao MW (2011) Rule acquisition and attribute reduction in real decision formal contexts. Soft Comput 15(6):1115–1128

    Article  MATH  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the anonymous reviewers for their valuable comments and helpful suggestions which lead to a significant improvement on the manuscript. This work was supported by the National Natural Science Foundation of China (Nos. 10971161, 61005042, 11071281 and 61202018).

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, People’s Republic of China

    Jinhai Li, Changlin Mei & Xiao Zhang

  2. School of Information Technology and Engineering, VIT University, Vellore, India

    Cherukuri Aswani Kumar

Authors
  1. Jinhai Li
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Changlin Mei
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Cherukuri Aswani Kumar
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Xiao Zhang
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Jinhai Li.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, J., Mei, C., Kumar, C.A. et al. On rule acquisition in decision formal contexts. Int. J. Mach. Learn. & Cyber. 4, 721–731 (2013). https://doi.org/10.1007/s13042-013-0150-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-013-0150-z

Keywords