Skip to main content
Log in

The conditional distributivity condition for T-uninorms revisited

  • Published:
Aequationes mathematicae Aims and scope Submit manuscript

Abstract

This paper studies the conditional distributivity for T-uninorms over uninorms in the most general setting, transforming it into the (conditional) distributivity equation involving two uninorms.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Aczél, J.: Lectures on Functional Equations and Their Applications. Acad. Press, New York (1966)

    MATH  Google Scholar 

  2. Calvo, T., Mayor, G., Mesiar, R.: Aggregation Operators: New Trends and Applications. Studies in Fuzziness and Soft Computing, vol. 97. Springer, Berlin (2002)

    Book  Google Scholar 

  3. Clifford, A.H.: Naturally totally ordered commutative semigroups. Am. J. Math. 76, 631C–646 (1954)

    Article  MathSciNet  Google Scholar 

  4. Dubois, D., Pap, E., Prade, H.: Hybrid probabilistic-possibilistic mixtures and utility functions. In: Fodor, J., De Baets, B., Perny, P. (eds.) Preferences and Decisions under Incomplete Knowledge. Studies in Fuzziness and Soft Computing, vol. 51, pp. 51–73. Physica, Heidelberg (2000)

    Chapter  Google Scholar 

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

  6. Jočić, D., Štajner-Papuga, I.: Distributivity and conditional distributivity for T-uninorms. Inf. Sci. 424, 91–103 (2018)

    Article  MathSciNet  Google Scholar 

  7. Jočić, D., Štajner-Papuga, I.: Some implications of the restricted distributivity of aggregation operators with absorbing elements for utility theory. Fuzzy Sets Syst. 291, 54–65 (2016)

    Article  MathSciNet  Google Scholar 

  8. Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Acad. Publ, Dordrecht (2000)

    Book  Google Scholar 

  9. Li, W., Qin, F.: Conditional distributivity equation for uninorms with continuous underlying operators. IEEE Trans. Fuzzy Syst. (2019). https://doi.org/10.1109/TFUZZ.2019.2920809

    Article  Google Scholar 

  10. Mas, M., Mesiar, R., Monserrat, M., Torrens, T.: Aggregation operations with annihilator. Int. J. Gen. Syst. 34(1), 17–38 (2005)

    Article  MathSciNet  Google Scholar 

  11. Mas, M., Massanet, S., Ruiz-Aguilera, D., Torrens, J.: A survey on the existing classes of uninorms. J. Intell. Fuzzy Syst. 29, 1021–1037 (2015)

    Article  MathSciNet  Google Scholar 

  12. 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  Google Scholar 

  13. Su, Y., Liu, H., Riera, J.V., Ruiz-Aguilera, D., Torrens, J.: The distributivity equation for uninorms revisited. Fuzzy Sets Syst. 334, 1–23 (2018)

    Article  MathSciNet  Google Scholar 

  14. Su, Y., Liu, H., Ruiz-Aguilera, D., Riera, J.V., Torrens, J.: On the distributivity property for uninorms. Fuzzy Sets Syst. 287, 184–202 (2016)

    Article  MathSciNet  Google Scholar 

  15. Su, Y., Zong, W., Wu, J.: Distributivity and conditional distributivity for uninorms with continuous underlying operators over a given continuous t-norm. IEEE Trans. Fuzzy Syst. (2020). https://doi.org/10.1109/TFUZZ.2020.2996378

    Article  Google Scholar 

  16. Yager, R.R., Rybalov, A.: Uninorm aggregation operators. Fuzzy Sets Syst. 80(1), 111–120 (1996)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant nos. 11901239,  11801220 and  12071259), the Natural Science Foundation of Shandong Province (Grant no. ZR2019BA005), and the Natural Science Foundation of Jiangsu Province (Grant no. BK20180590).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wenwen Zong.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work is supported by the National Natural Science Foundation of China (Grant Nos. 11901239,  11801220 and  12071259), the Natural Science Foundation of Shandong Province (Grant No. ZR2019BA005), and the Natural Science Foundation of Jiangsu Province (Grant No. BK20180590).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zong, W., Su, Y. The conditional distributivity condition for T-uninorms revisited. Aequat. Math. 95, 931–939 (2021). https://doi.org/10.1007/s00010-020-00769-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00010-020-00769-4

Keywords

Mathematics Subject Classification

Navigation