Skip to main content

Algorithms for Computation of Concept Trilattice of Triadic Fuzzy Context

  • Conference paper
Advances in Computational Intelligence (IPMU 2012)

Abstract

Triadic concept analysis (TCA) is a method of relational data analysis whose aim is to extract a hierarchically structured set of particular clusters from a three-way data describing objects, attributes, and conditions. We present two algorithms for the problem of computing all such clusters from a data describing degrees to which objects have attributes under conditions.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Belohlavek, R.: Fuzzy Galois connections. Math. Logic Quarterly 45(4), 497–504 (1999) ISSN 0942-5616

    Article  MathSciNet  MATH  Google Scholar 

  2. Belohlavek, R.: Reduction and a simple proof of characterization of fuzzy concept lattices. Fundamenta Informaticae 46(4), 277–285 (2001) ISSN 0169-2968

    Google Scholar 

  3. Belohlavek, R.: Fuzzy Relational Systems: Foundations and Principles. Kluwer, Academic/Plenum Publishers, New York (2002)

    MATH  Google Scholar 

  4. Belohlavek, R.: Algorithms for fuzzy concept lattices. In: Proc. Fourth Int. Conf. on Recent Advances in Soft Computing, RASC 2002, Nottingham, United Kingdom, December 12-13, pp. 200–205 (2002)

    Google Scholar 

  5. Belohlavek, R., Vychodil, V.: What is a fuzzy concept lattice? In: Proc. CLA 2005, 3rd Int. Conference on Concept Lattices and Their Applications, September 7-9, pp. 34–45. Czech Republic, Olomouc (2005) ISBN 80-248-0863-3

    Google Scholar 

  6. Belohlavek, R., De Baets, B., Outrata, J., Vychodil, V.: Computing the lattice of all fixpoints of a fuzzy closure operator. IEEE Transactions on Fuzzy Systems 18(3), 546–557 (2010)

    Article  Google Scholar 

  7. Belohlavek, R.: Optimal decompositions of matrices with entries from residuated lattices. J. Logic and Computation (September 7, 2011), doi:10.1093/logcom/exr023

    Google Scholar 

  8. Belohlavek, R., Osicka, P.: Triadic concept lattices of data with graded attributes. International Journal of General Systems (December 12, 2011), doi:10.1080/03081079.2011.643548

    Google Scholar 

  9. Belohlavek, R., Osička, P., Vychodil, V.: Factorizing Three-Way Ordinal Data Using Triadic Formal Concepts. In: Christiansen, H., De Tré, G., Yazici, A., Zadrozny, S., Andreasen, T., Larsen, H.L. (eds.) FQAS 2011. LNCS, vol. 7022, pp. 400–411. Springer, Heidelberg (2011), doi:10.1007/978-3-642-24764-4_35

    Chapter  Google Scholar 

  10. Biedermann, K.: An equational theory for trilattices. In: Algebra Universalis, vol. 42. Birkhäuser, Basel (1999)

    Google Scholar 

  11. Biedermann, K.: Triadic Galois Connections Triadic Galois connections. In: Denecke, K., Lüders, O. (eds.) General Algebra and Applications in Discrete Mathematics, pp. 23–33. Shaker, Aachen (1997)

    Google Scholar 

  12. Ganter, B., Wille, R.: Formal Concept Analysis. Mathematical Foundations. Springer, Berlin (1999)

    Book  MATH  Google Scholar 

  13. Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht (1998)

    Book  MATH  Google Scholar 

  14. Jäschke, R., Hotho, A., Schmitz, C., Ganter, B., Stumme, G.: TRIAS – An Algorithm for Mining Iceberg Tri-Lattices. In: ICDM 2006, pp. 907–911 (2006)

    Google Scholar 

  15. Kolda, T.G., Bader, B.W.: Tensor decompositions and applications. SIAM Review 51(3), 455–500 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Kroonenberg, P.M.: Applied Multiway Data Analysis. J. Wiley (2008)

    Google Scholar 

  17. Lehmann, F., Wille, R.: A Triadic Approach to Formal Concept Analysis. In: Ellis, G., Rich, W., Levinson, R., Sowa, J.F. (eds.) ICCS 1995. LNCS, vol. 954, pp. 32–43. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  18. Pollandt, S.: Fuzzy Begriffe. Springer, Berlin (1997)

    Book  MATH  Google Scholar 

  19. Smilde, A., Bro, R., Geladi, P.: Multi-way Analysis: Applications in the Chemical Sciences. J. Wiley (2004)

    Google Scholar 

  20. Ward, M., Dilworth, R.P.: Residuated lattices. Trans. Amer. Math. Soc. 45, 335–354 (1939)

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

  22. Wille, R.: The basic theorem of triadic concept analysis. Order 12, 149–158 (1995)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Osicka, P. (2012). Algorithms for Computation of Concept Trilattice of Triadic Fuzzy Context. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31718-7_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31718-7_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31717-0

  • Online ISBN: 978-3-642-31718-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics