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A classification of barycentrically associative polynomial functions

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Abstract

We describe the class of polynomial functions which are barycentrically associative over an infinite commutative integral domain.

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References

  1. Antoine, C., Moyennes, L.: Que sais-je?, vol. 3383. Presse Universitaires de France, Paris (1998)

  2. de Finetti B.: Sul concetto di media. G. Inst. Ital. Attari 2(3), 369–396 (1931)

    Google Scholar 

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

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

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

    MATH  Google Scholar 

  6. Nagumo M.: Über eine klasse der mittelwerte (German). Jpn. J.Math. 7, 71–79 (1930)

    MATH  Google Scholar 

  7. Schimmack R.: Der Satz vom arithmetischen Mittel in axiomatischer Begründung. Math. Ann. 68, 125–132 (1909)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

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

    Jean-Luc Marichal & Jörg Tomaschek

  2. Department of Mathematics, University of Liège, Grande Traverse, 12-B37, 4000, Liege, Belgium

    Pierre Mathonet

Authors
  1. Jean-Luc Marichal
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  2. Pierre Mathonet
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  3. Jörg Tomaschek
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Correspondence to Jean-Luc Marichal.

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Marichal, JL., Mathonet, P. & Tomaschek, J. A classification of barycentrically associative polynomial functions. Aequat. Math. 89, 1281–1291 (2015). https://doi.org/10.1007/s00010-014-0332-0

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  • DOI: https://doi.org/10.1007/s00010-014-0332-0

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