Skip to main content

On Migrative t-Conorms and Uninorms

  • Conference paper

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 299))

Abstract

In this paper the notions of α-migrative t-conorms over a fixed t-conorm S 0, and α-migrative uninorms over another fixed uninorm U 0 with the same neutral element are introduced. All continuous t-conorms that are α-migrative over the maximum, the probabilistic sum and the Łukasiewicz t-conorm are characterized. Uninorms belonging to one of the classes \({\cal U}_{\min}\), \({\cal U}_{\max}\), idempotent or representable that are α-migrative over a uninorm U 0 in \( {\cal U}_{\min}\) or \({\cal U}_{\max}\) are also characterized.

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

Buying options

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. Alsina, C., Frank, M.J., Schweizer, B.: Associative Functions. Triangular Norms and Copulas. World Scientific, New Jersey (2006)

    Book  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  3. Beliakov, G., Calvo, T.: On migrative means and copulas. In: Proceedings of the AGOP 2009, pp. 107–110. Palma de Mallorca (2009)

    Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. Calvo, T., De Baets, B., Fodor, J.: The functional equations of Frank and Alsina for uninorms and nullnorms. Fuzzy Sets and Systems 120, 385–394 (2001)

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  9. Drygaś, P.: On properties of uninorms with underlying t-norm and t-conorms given as ordinal sums. Fuzzy Sets and Systems 161, 149–157 (2010)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  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  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  16. 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 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  19. Mas, M., Mayor, G., Torrens, J.: The distributivity condition for uninorms and t-operators. Fuzzy Sets and Systems 128, 209–225 (2002)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  21. Xie, A., Liu, H.: Solutions to the extended migrative functional equation based on continuous triangular norms (2011) (preprint)

    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

Mas, M., Monserrat, M., Ruiz-Aguilera, D., Torrens, J. (2012). On Migrative t-Conorms and Uninorms. 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_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31718-7_30

  • 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