Skip to main content
SpringerLink
Log in

A Characterization of Barycentrically Preassociative Functions

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

We provide a characterization of the variadic functions which are barycentrically preassociative as compositions of length-preserving associative string functions with one-to-one unary maps. We also discuss some consequences of this characterization.

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. de Finetti B.: Sul concetto di media. Giornale dell’ Instituto Italiano degli Attari 2(3), 369–396 (1931)

    Google Scholar 

  2. Fodor J., Roubens M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer, Dordrecht (1994)

    Book  MATH  Google Scholar 

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

    Google Scholar 

  4. Kolmogoroff A.N.: Sur la notion de la moyenne (French). Atti Accad. Naz. Lincei 12(6), 388–391 (1930)

    MATH  Google Scholar 

  5. Lehtonen, E., Marichal, J.-L., Teheux, B.: Associative string functions. Asian-Eur. J. Math. 7(4), 1450059 (2014) (18 pages)

  6. Marichal, J.-L., Teheux, B.: Associative and preassociative functions. Semigroup Forum 89(2), 431–442 (2014) (improved version available at arXiv:1309.7303v3)

  7. Marichal J.-L., Teheux B.: Preassociative aggregation functions. Fuzzy Sets Syst. 268, 15–26 (2015)

    Article  MathSciNet  Google Scholar 

  8. Marichal J.-L., Teheux B.: Barycentrically associative and preassociative functions. Acta Math. Hung. 145(2), 468–488 (2015)

    Article  MathSciNet  Google Scholar 

  9. Nagumo M.: Über eine Klasse der Mittelwerte (German). Jpn. J. Math. 7, 71–79 (1930)

    MATH  Google Scholar 

  10. Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. North-Holland Series in Probability and Applied Mathematics. North-Holland Publishing Co., New York (1983) [new edition in: Dover Publications, New York (2005)]

Download references

Author information

Authors and Affiliations

  1. Mathematics Research Unit, FSTC, University of Luxembourg, 6, rue Coudenhove-Kalergi, 1359, Luxembourg, Luxembourg

    Jean-Luc Marichal & Bruno Teheux

Authors
  1. Jean-Luc Marichal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bruno Teheux
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bruno Teheux.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Marichal, JL., Teheux, B. A Characterization of Barycentrically Preassociative Functions. Results. Math. 69, 245–256 (2016). https://doi.org/10.1007/s00025-015-0501-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00025-015-0501-z

Mathematics Subject Classification

Keywords

Search

Navigation