Skip to main content
SpringerLink
Log in
Book cover

International Conference on Formal Concept Analysis

ICFCA 2014: Formal Concept Analysis pp 67–79Cite as

On the Existence of Isotone Galois Connections between Preorders

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8478))

Abstract

Given a mapping f : A → B from a preordered set A into an unstructured set B, we study the problem of defining a suitable preordering relation on B such that there exists a mapping g : B → A such that the pair (f,g) forms an adjunction between preordered sets.

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

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Antoni, L., Krajči, S., Krídlo, O., Macek, B., Pisková, L.: On heterogeneous formal contexts. Fuzzy Sets and Systems 234, 22–33 (2014)

    Article  MathSciNet  Google Scholar 

  2. Bělohlávek, R.: Fuzzy Galois connections. Mathematical Logic Quarterly 45(4), 497–504 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bělohlávek, R., Konečný, J.: Concept lattices of isotone vs. antitone Galois connections in graded setting: Mutual reducibility revisited. Information Sciences 199, 133–137 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bělohlávek, R., Osička, P.: Triadic fuzzy Galois connections as ordinary connections. In: IEEE Intl Conf. on Fuzzy Systems (2012)

    Google Scholar 

  5. Blyth, T.S.: Lattices and Ordered Algebraic Structures. Springer (2005)

    Google Scholar 

  6. Butka, P., Pócs, J., Pócsová, J.: On equivalence of conceptual scaling and generalized one-sided concept lattices. Information Sciences 259, 57–70 (2014)

    Article  MathSciNet  Google Scholar 

  7. Castellini, G., Koslowski, J., Strecker, G.: Closure operators and polarities. Annals of the New York Academy of Sciences 704, 38–52 (1993)

    Article  MathSciNet  Google Scholar 

  8. Cohen, D.A., Creed, P., Jeavons, P.G., Živný, S.: An algebraic theory of complexity for valued constraints: Establishing a Galois connection. In: Murlak, F., Sankowski, P. (eds.) MFCS 2011. LNCS, vol. 6907, pp. 231–242. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  9. Denecke, K., Erné, M., Wismath, S.L.: Galois connections and applications, vol. 565. Springer (2004)

    Google Scholar 

  10. Díaz, J.C., Medina, J.: Multi-adjoint relation equations: Definition, properties and solutions using concept lattices. Information Sciences 253, 100–109 (2013)

    Article  MathSciNet  Google Scholar 

  11. Dubois, D., Prade, H.: Possibility theory and formal concept analysis: Characterizing independent sub-contexts. Fuzzy Sets and Systems 196, 4–16 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  12. Dzik, W., Järvinen, J., Kondo, M.: Intuitionistic propositional logic with Galois connections. Logic Journal of the IGPL 18(6), 837–858 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  13. Dzik, W., Järvinen, J., Kondo, M.: Representing expansions of bounded distributive lattices with Galois connections in terms of rough sets. International Journal of Approximate Reasoning 55(1), 427–435 (2014)

    Article  MathSciNet  Google Scholar 

  14. Frascella, A.: Fuzzy Galois connections under weak conditions. Fuzzy Sets and Systems 172(1), 33–50 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  15. Galitsky, B.A., Kovalerchuk, B., Kuznetsov, S.O.: Learning Common Outcomes of Communicative Actions Represented by Labeled Graphs. In: Priss, U., Polovina, S., Hill, R. (eds.) ICCS 2007. LNCS (LNAI), vol. 4604, pp. 387–400. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  16. Ganter, B., Kuznetsov, S.O.: Pattern Structures and Their Projections. In: Delugach, H.S., Stumme, G. (eds.) ICCS 2001. LNCS (LNAI), vol. 2120, pp. 129–142. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  17. García-Pardo, F., Cabrera, I.P., Cordero, P., Ojeda-Aciego, M.: On Galois Connections and Soft Computing. In: Rojas, I., Joya, G., Cabestany, J. (eds.) IWANN 2013, Part II. LNCS, vol. 7903, pp. 224–235. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  18. García-Pardo, F., Cabrera, I.P., Cordero, P., Ojeda-Aciego, M., Rodríguez, F.J.: Generating isotone Galois connections on an unstructured codomain. In: Proc. of Information Processing and Management of Uncertainty in Knowledge-based Systems, IPMU (to appear, 2014)

    Google Scholar 

  19. Guo, L., Zhang, G.-Q., Li, Q.: Fuzzy closure systems on L-ordered sets. Mathematical Logic Quarterly 57(3), 281–291 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  20. Järvinen, J.: Pawlak’s information systems in terms of Galois connections and functional dependencies. Fundamenta Informaticae 75, 315–330 (2007)

    MATH  MathSciNet  Google Scholar 

  21. Järvinen, J., Kondo, M., Kortelainen, J.: Logics from Galois connections. Int. J. Approx. Reasoning 49(3), 595–606 (2008)

    Article  MATH  Google Scholar 

  22. Kaytoue, M., Kuznetsov, S.O., Napoli, A., Duplessis, S.: Mining gene expression data with pattern structures in formal concept analysis. Information Sciences 181(10), 1989–2001 (2011)

    Article  MathSciNet  Google Scholar 

  23. Kan, D.M.: Adjoint functors. Transactions of the American Mathematical Society 87(2), 294–329 (1958)

    Article  MATH  MathSciNet  Google Scholar 

  24. Kerkhoff, S.: A general Galois theory for operations and relations in arbitrary categories. Algebra Universalis 68(3), 325–352 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  25. Konecny, J.: Isotone fuzzy Galois connections with hedges. Information Sciences 181(10), 1804–1817 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  26. Kuznetsov, S.O.: Fitting Pattern Structures to Knowledge Discovery in Big Data. In: Cellier, P., Distel, F., Ganter, B. (eds.) ICFCA 2013. LNCS, vol. 7880, pp. 254–266. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  27. Medina, J.: Multi-adjoint property-oriented and object-oriented concept lattices. Information Sciences 190, 95–106 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  28. Melton, A., Schmidt, D.A., Strecker, G.E.: Galois connections and computer science applications. In: Poigné, A., Pitt, D.H., Rydeheard, D.E., Abramsky, S. (eds.) Category Theory and Computer Programming. LNCS, vol. 240, pp. 299–312. Springer, Heidelberg (1986)

    Chapter  Google Scholar 

  29. Mu, S.-C., Oliveira, J.N.: Programming from Galois connections. The Journal of Logic and Algebraic Programming 81(6), 680–704 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  30. Ore, Ø.: Galois connections. Transactions of the American Mathematical Society 55, 493–513 (1944)

    Article  MATH  MathSciNet  Google Scholar 

  31. Poelmans, J., Ignatov, D.I., Kuznetsov, S.O., Dedene, G.: Fuzzy and rough formal concept analysis: a survey. Intl Journal of General Systems 43(2), 105–134 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  32. Restrepo, M., Cornelis, C., Gómez, J.: Duality, conjugacy and adjointness of approximation operators in covering-based rough sets. Intl. Journal of Approximate Reasoning 55(1), 469–485 (2014)

    Article  Google Scholar 

  33. Valverde-Albacete, F.J., Peláez-Moreno, C.: Extending conceptualisation modes for generalised formal concept analysis. Information Sciences 181, 1888–1909 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  34. Wolski, M.: Galois connections and data analysis. Fundamenta Informaticae 60, 401–415 (2004)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universidad de Málaga, Spain

    Francisca García-Pardo, Inma P. Cabrera, Pablo Cordero, Manuel Ojeda-Aciego & Francisco J. Rodríguez-Sanchez

Authors
  1. Francisca García-Pardo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Inma P. Cabrera
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pablo Cordero
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Manuel Ojeda-Aciego
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Francisco J. Rodríguez-Sanchez
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Technische Universität Dresden, 01062, Dresden, Germany

    Cynthia Vera Glodeanu

  2. INSA-Lyon, CNRS, LIRIS UMR 5205, 9621, 69621, Lyon, France

    Mehdi Kaytoue

  3. Babes-Bolyai University, 400084, Cluj, Romania

    Christian Sacarea

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

García-Pardo, F., Cabrera, I.P., Cordero, P., Ojeda-Aciego, M., Rodríguez-Sanchez, F.J. (2014). On the Existence of Isotone Galois Connections between Preorders. In: Glodeanu, C.V., Kaytoue, M., Sacarea, C. (eds) Formal Concept Analysis. ICFCA 2014. Lecture Notes in Computer Science(), vol 8478. Springer, Cham. https://doi.org/10.1007/978-3-319-07248-7_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-07248-7_6

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07247-0

  • Online ISBN: 978-3-319-07248-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation