Skip to main content
SpringerLink
Log in
Book cover

International Conference on Formal Concept Analysis

ICFCA 2007: Formal Concept Analysis pp 197–209Cite as

On Multi-adjoint Concept Lattices: Definition and Representation Theorem

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNAI,volume 4390)

Abstract

Several fuzzifications of formal concept analysis have been proposed to deal with uncertainty or incomplete information. In this paper, we focus on the new paradigm of multi-adjoint concept lattices which embeds different fuzzy extensions of concept lattices, our main result being the representation theorem of this paradigm. As a consequence of this theorem, the representation theorems of the other paradigms can be proved more directly. Moreover, the multi-adjoint paradigm enriches the language providing greater flexibility to the user.

Keywords

  • concept lattices
  • multi-adjoint lattices
  • Galois connection
  • implication triples

This is a preview of subscription content, access via your institution.

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abdel-Hamid, A., Morsi, N.: Associatively tied implicacions. Fuzzy Sets and Systems 136(3), 291–311 (2003)

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Bělohlávek, R.: Fuzzy concepts and conceptual structures: induced similarities. In: Joint Conference on Information Sciences, pp. 179–182 (1998)

    Google Scholar 

  3. Bělohlávek, R.: Lattices of fixed points of fuzzy galois connections. Mathematical Logic Quartely 47(1), 111–116 (2001)

    CrossRef  MATH  Google Scholar 

  4. Bělohlávek, R.: Reduction and a simple proof of characterization of fuzzy concept lattices. Fundamenta Informaticae 46(4), 277–285 (2001)

    MathSciNet  MATH  Google Scholar 

  5. Bělohlávek, R.: Concept lattices and order in fuzzy logic. Annals of Pure and Applied Logic 128, 277–298 (2004)

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Bělohlávek, R., Vychodil, V.: What is a fuzzy concept lattice? In: 3rd Intl. Conf. on Concept Lattices and their Applications, pp. 34–45 (2005)

    Google Scholar 

  7. Burusco, A., Fuentes-González, R.: The study of L-fuzzy concept lattice. Mathware & Soft Computing 3, 209–218 (1994)

    Google Scholar 

  8. Burusco, A., Fuentes-González, R.: Concept lattices defined from implication operators. Fuzzy Sets and Systems 114, 431–436 (2000)

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Davey, B., Priestley, H.: Introduction to Lattices and Order, 2nd edn. Cambridge University Press, Cambridge (2002)

    MATH  Google Scholar 

  10. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundation. Springer, Heidelberg (1999)

    Google Scholar 

  11. Georgescu, G., Popescu, A.: Concept lattices and similarity in non-commutative fuzzy logic. Fundamenta Informaticae 55(1), 23–54 (2002)

    MathSciNet  Google Scholar 

  12. Georgescu, G., Popescu, A.: Non-commutative fuzzy galois connections. Soft Comput. 7(7), 458–467 (2003)

    MATH  Google Scholar 

  13. Georgescu, G., Popescu, A.: Non-dual fuzzy connections. Arch. Math. Log. 43(8), 1009–1039 (2004)

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Georgescu, G., Popescu, A.: Similarity convergence in residuated structures. Logic Journal of the IGPL 13(4), 389–413 (2005)

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. Hájek, P.: Metamathematics of Fuzzy Logic. In: Trends in Logic. Studia Logica Library, Kluwer Academic Publishers, Dordrecht (1998)

    Google Scholar 

  16. Julián, P., Moreno, G., Penabad, J.: On fuzzy unfolding: A multi-adjoint approach. Fuzzy Sets and Systems 154, 16–33 (2005)

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. Krajči, S.: The basic theorem on generalized concept lattice. In: Snášel, V., Bělohlávek, R. (eds.) ERCIM workshop on soft computing, pp. 25–33 (2004)

    Google Scholar 

  18. Krajči, S.: A generalized concept lattice. Logic Journal of IGPL 13(5), 543–550 (2005)

    CrossRef  MATH  Google Scholar 

  19. Medina, J., et al.: Towards biresiduated multi-adjoint logic programming. In: Conejo, R., Urretavizcaya, M., Pérez-de-la-Cruz, J.-L. (eds.) Current Topics in Artificial Intelligence. LNCS (LNAI), vol. 3040, pp. 608–617. Springer, Heidelberg (2004)

    Google Scholar 

  20. Medina, J., Ojeda-Aciego, M., Vojtáš, P.: Multi-adjoint logic programming with continuous semantics. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 351–364. Springer, Heidelberg (2001)

    Google Scholar 

  21. Medina, J., Ojeda-Aciego, M., Vojtáš, P.: Similarity-based unification: a multi-adjoint approach. Fuzzy Sets and Systems 146(1), 43–62 (2004)

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. Medina, J., Ruiz-Calviño, J.: Towards multi-adjoint concept lattices. In: Information Processing and Management of Uncertainty for Knowledge-Based Systems, IPMU’06, pp. 2566–2571 (2006)

    Google Scholar 

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

    MATH  Google Scholar 

  24. Umbreit, S.: Formale Begriffsanalyse mit unscharfen Begriffen. PhD thesis, Halle, Saale (1995)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. Matemática Aplicada. Universidad de Málaga,  

    Jesús Medina, Manuel Ojeda-Aciego & Jorge Ruiz-Calviño

Authors
  1. Jesús Medina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Manuel Ojeda-Aciego
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jorge Ruiz-Calviño
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Sergei O. Kuznetsov Stefan Schmidt

Rights and permissions

Reprints and Permissions

Copyright information

© 2007 Springer Berlin Heidelberg

About this paper

Cite this paper

Medina, J., Ojeda-Aciego, M., Ruiz-Calviño, J. (2007). On Multi-adjoint Concept Lattices: Definition and Representation Theorem. In: Kuznetsov, S.O., Schmidt, S. (eds) Formal Concept Analysis. ICFCA 2007. Lecture Notes in Computer Science(), vol 4390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70901-5_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-70901-5_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70828-5

  • Online ISBN: 978-3-540-70901-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

search

Navigation