Skip to main content
SpringerLink
Log in

The cross-migrative property for uninorms

  • Published:
Aequationes mathematicae Aims and scope Submit manuscript

Abstract

This paper aims to study the cross-migrative property for uninorms. We only consider the most usual classes of uninorms as follows: uninorms in \({\mathcal{U}_{min}}\) and \({\mathcal{U}_{max}}\), representable uninorms, idempotent uninorms and uninorms continuous in the open unit square, and limit the research to those uninorms which have the same neutral element. This study shows that there is no cross-migrativity between representable uninorms and other classes of uninorms. The relationship is the same between conjunctive uninorms and disjunctive uninorms. We give the sufficient and necessary conditions for the cross-migrativity equation to hold for all of the other possible combinations of uninorms.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  3. De Baets B.: Idempotent uninorms. Eur. J. Oper. Res. 118, 631–642 (1999)

    Article  MATH  Google Scholar 

  4. Durante F., Sarkoci P.: A note on the convex combinations of triangular norms. Fuzzy Sets Syst. 159, 77–80 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Durante F., Ricci R.G.: Supermigrative semi-copulas and triangular norms. Inf. Sci. 179, 2689–2694 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Fodor J., Klement E.P., Mesiar R.: Cross-migrative triangular norms. Int. J. Intell. Syst. 27, 411–428 (2012)

    Article  Google Scholar 

  7. Fodor J., Yager R., Rybalov A.: Structure of Uninorms. Int. J. Uncertain. Fuzziness Knowl Based Syst. 5, 411–428 (1997)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Book  MATH  Google Scholar 

  12. Klement E.P., Mesiar R., Pap E.: On the relationship of associative compensatory operators to triangular norms and conorms. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 4, 129–144 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  13. Li S., Qin F., Fodor J.: On the cross-migrativity with respect to continuous t-norms. Int. J. Intell. Syst. 30, 550–562 (2015)

    Article  Google Scholar 

  14. Lopez-Molina, C., De Baets, B., Bustince, H., et al.: Bimigrativity of binary aggregation functions. Inf. Sci. 274, 225–235 (2014)

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

    Article  MathSciNet  MATH  Google Scholar 

  16. Mas M., Monserrat M., Ruiz-Aguilera D., Torrens J.: On migrative t-conorms and uninorms. Commun. Comput. Inf. Sci. 299, 286–295 (2012)

    MATH  Google Scholar 

  17. Mas M., Monserrat M., Ruiz-Aguilera D., Torrens J.: An extension of the migrative property for uninorms. Inf. Sci. 246, 191–198 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  18. Mas M., Monserrat M., Ruiz-Aguilera D., Torrens J.: Migrative uninorms and nullnorms over t-norms and t-conorms. Fuzzy Sets Syst. 261, 20–32 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  19. Ouyang Y.: Generalizing the migrativity of continuous t-norms. Fuzzy Sets Syst. 211, 73–83 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  20. Pap E.: An integral generated by decomposable measure. Univ. Novom Sadu Zb. Rad. Prirod. Mat. Fak. Ser. Mat. 20, 135–144 (1990)

    MathSciNet  MATH  Google Scholar 

  21. Pap E.: Pseudo-additive measures and their applications. Handb. Measure Theory II, 1403–1465 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  22. Ruiz-Aguilera, D., Torrens, J., De Baets, B., Fodor, J.: Some remarks on the characterization of idempotent uninorms. In: Proceedings of the Computational intelligence for knowledge-based systems design, and 13th international conference on Information processing and management of uncertainty, pp. 425–434. Springer, New York (2010)

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

    Article  MATH  Google Scholar 

  24. Su Y., Zong W., Liu H.W.: Migrativity property for uninorms. Fuzzy Sets Syst. 287, 213–226 (2016)

    Article  MathSciNet  Google Scholar 

  25. Su Y., Zong W., Liu H.W., Xue P.J.: Migrativity property for uninorms and semi t-operators. Inf. Sci. 325, 455–465 (2015)

    Article  MathSciNet  Google Scholar 

  26. Su Y., Zong W., Liu H.W., Zhang F.X.: On migrativity property for uninorms. Inf. Sci. 300, 114–123 (2015)

    Article  MathSciNet  Google Scholar 

  27. Wang, H.D., Qin, F.: On the cross-migrativity of triangular subnorms. In: 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 1139–1142 (2014)

  28. Yager R., Rybalov A.: Uninorm aggregation operators. Fuzzy Sets Syst. 80, 111–120 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  29. Zong W., Su Y., Liu H.W.: Migrativity property for nullnorms. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 22, 749–759 (2014)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, People’s Republic of China

    Hang Zhan & Hua-Wen Liu

Authors
  1. Hang Zhan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hua-Wen Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hua-Wen Liu.

Additional information

This work is supported by the National Natural Foundation of China (Nos. 61573211 and 61174099) and the Research Found for the Doctoral Program of Higher Education of China (No. 20120131110001).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhan, H., Liu, HW. The cross-migrative property for uninorms. Aequat. Math. 90, 1219–1239 (2016). https://doi.org/10.1007/s00010-016-0437-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00010-016-0437-8

Mathematics Subject Classification

Keywords

Search

Navigation