On integer-valued means and the symmetric maximum

Miguel Couceiro () and Michel Grabisch
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Miguel Couceiro: ORPAILLEUR - Knowledge representation, reasonning - Centre Inria de l'Université de Lorraine - 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

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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.

Keywords: integer means; nonassociative algebra; symmetric maximum; decomposability; moyenne sue les entiers; algèbre non associative; décomposabilité (search for similar items in EconPapers)
Date: 2016-09
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01412025v1
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Published in 2016

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Related works:
Working Paper: On integer-valued means and the symmetric maximum (2016)
Working Paper: On integer-valued means and the symmetric maximum (2016)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-01412025

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