Skip to main content
SpringerLink
Log in

Migrativity of Uninorms over T-norms and T-conorms

  • Conference paper
Aggregation Functions in Theory and in Practise

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 228))

Abstract

In this paper the notions of α-migrative uninorms over a fixed t-norm T and over a fixed t-conorm S are introduced and studied. All cases when the uninorm U lies in any one of the most usual classes of uninorms are analyzed, characterizing with some assumptions on continuity all solutions of the migrativity equation for all possible combinations of U and T and for all possible combinations of U and S.

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

Access this chapter

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 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
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. Alsina, C., Frank, M.J., Schweizer, B.: Associative Functions. Triangular Norms and Copulas. World Scientific, New Jersey (2006)

    Book  MATH  Google Scholar 

  2. Beliakov, G., Calvo, T.: On migrative means and copulas. In: Proceedings of Fifth International Summer School on Aggregation Operators, AGOP 2009, Palma de Mallorca, pp. 107–110 (2009)

    Google Scholar 

  3. Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practicioners. Springer, Heidelberg (2007)

    Google Scholar 

  4. Bustince, H., De Baets, B., Fernandez, J., Mesiar, R., Montero, J.: A generalization of the migrativity property of aggregation functions. Information Sciences 191, 76–85 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bustince, H., Montero, J., Mesiar, R.: Migrativity of aggregation functions. Fuzzy Sets and Systems 160, 766–777 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  6. Calvo, T., Mayor, G., Mesiar, R. (eds.): Aggregation operators. New trends and applications. STUDFUZZ, vol. 97. Physica-Verlag, Heidelberg (2002)

    MATH  Google Scholar 

  7. De Baets, B.: Idempotent uninorms. European Journal of Operational Research 118, 631–642 (1999)

    Article  MATH  Google Scholar 

  8. Durante, F., Ricci, R.G.: Supermigrative semi-copulas and triangular norms. Information Sciences 179, 2689–2694 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  9. Durante, F., Sarkoci, P.: A note on the convex combination of triangular norms. Fuzzy Sets and Systems 159, 77–80 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  10. Fodor, J., De Baets, B.: A single-point characterization of representable uninorms. Fuzzy Sets and Systems 202, 89–99 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  11. Fodor, J., Rudas, I.J.: On continuous triangular norms that are migrative. Fuzzy Sets and Systems 158, 1692–1697 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  12. Fodor, J., Rudas, I.J.: An extension of the migrative property for triangular norms. Fuzzy Sets and Systems 168, 70–80 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  13. Fodor, J., Rudas, I.J.: Migrative t-norms with respect to continuous ordinal sums. Information Sciences 181, 4860–4866 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  14. Fodor, J., Yager, R.R., Rybalov, A.: Structure of uninorms. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 5, 411–427 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  15. Grabisch, M., Marichal, J.L., Mesiar, R., Pap, E.: Aggregation functions. In: Encyclopedia of Mathematics and its Applications, vol. 127. Cambridge University Press (2009)

    Google Scholar 

  16. Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. Kluwer Academic Publishers, Dordrecht (2000)

    Book  MATH  Google Scholar 

  17. Hu, S.K., Li, Z.F.: The structure of continuous uninorms. Fuzzy Sets and Systems 124, 43–52 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  18. Martín, J., Mayor, G., Torrens, J.: On locally internal monotonic operations. Fuzzy Sets and Systems 137, 27–42 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  19. Mas, M., Monserrat, M., Ruiz-Aguilera, D., Torrens, J.: On migrative t-conorms and uninorms. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds.) IPMU 2012, Part III. CCIS, vol. 299, pp. 286–295. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  20. Mas, M., Monserrat, M., Ruiz-Aguilera, D., Torrens, J.: An extension of the migrative property for uninorms. Information Sciences (2012) (submitted)

    Google Scholar 

  21. Mesiar, R., Bustince, H., Fernandez, J.: On the α-migrativity of semicopulas, quasi-copulas and copulas. Information Sciences 180, 1967–1976 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  22. Ricci, R.G.: Supermigrative aggregation functions. In: Proceedings of the 6th International Summer School on Aggregation Operators, AGOP 2011, Benevento, Italy, pp. 145–150 (2011)

    Google Scholar 

  23. Ruiz, D., Torrens, J.: Distributivity and conditional distributivity of a uninorm and a continuous t-conorm. IEEE Transactions on Fuzzy Systems 14, 180–190 (2006)

    Article  Google Scholar 

  24. Ruiz-Aguilera, D., Torrens, J., De Baets, B., Fodor, J.: Some remarks on the characterization of idempotent uninorms. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. LNCS (LNAI), vol. 6178, pp. 425–434. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Carretera de Valldemossa, Universitat de les Illes Balears, km 7.5, 07122, Palma, Spain

    M. Mas, M. Monserrat, D. Ruiz-Aguilera & J. Torrens

Authors
  1. M. Mas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Monserrat
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. Ruiz-Aguilera
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. Torrens
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Mas .

Editor information

Editors and Affiliations

  1. Department of Automatica y Computacion, Universidad Publica de Navarra, Pamplona, Spain

    Humberto Bustince

  2. Department of Automatica y Computacion, Universidad Publica de Navarra, Pamplona, Spain

    Javier Fernandez

  3. Department of Mathematics and, Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  4. Department of Computer Science, Universidad de Alcalá de Henares, Madrid, Spain

    Tomasa Calvo

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mas, M., Monserrat, M., Ruiz-Aguilera, D., Torrens, J. (2013). Migrativity of Uninorms over T-norms and T-conorms. In: Bustince, H., Fernandez, J., Mesiar, R., Calvo, T. (eds) Aggregation Functions in Theory and in Practise. Advances in Intelligent Systems and Computing, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39165-1_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-39165-1_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39164-4

  • Online ISBN: 978-3-642-39165-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation