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On integer-valued means and the symmetric maximum

Author

Listed:
  • Miguel Couceiro

    (ORPAILLEUR - Knowledge representation, reasonning - Inria Nancy - Grand Est - Inria - Institut National de Recherche en Informatique et en Automatique - LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery - LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications - Inria - Institut National de Recherche en Informatique et en Automatique - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique)

  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

Integer-valued means, satisfying the decomposability condition of Kolmogoroff/Nagumo, are necessarily extremal, i.e., the mean value depends only on the minimal and maximal inputs. To overcome this severe limitation, we propose an infinite family of (weak) integer means based on the symmetric maximum and computation rules. For such means, their value depends not only on extremal inputs, but also on 2nd, 3rd, etc…, extremal values as needed. In particular, we show that this family can be characterized by a weak version of decomposability.

Suggested Citation

  • Miguel Couceiro & Michel Grabisch, 2016. "On integer-valued means and the symmetric maximum," Post-Print halshs-01412025, HAL.
    • Handle: RePEc:hal:journl:halshs-01412025
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01412025
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    References listed on IDEAS

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    1. Miguel Couceiro & Michel Grabisch, 2013. "On the poset of computation rules for nonassociative calculus," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00787750, HAL.
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    1. Miguel Couceiro & Michel Grabisch, 2016. "On integer-valued means and the symmetric maximum," Documents de travail du Centre d'Economie de la Sorbonne 16080, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

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