Aequationes mathematicae

, Volume 91, Issue 2, pp 353–371 | Cite as

On integer-valued means and the symmetric maximum

  • Miguel Couceiro
  • Michel GrabischEmail author


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.


Integer means nonassociative algebra symmetric maximum decomposability 

Mathematics Subject Classification

26E60 08A99 06A99 


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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.LORIA (CNRS-Inria Nancy Grand Est-Université de Lorraine)Vandoeuvre-lès-NancyFrance
  2. 2.Paris School of EconomicsUniversity of Paris IParisFrance

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