On comparison meaningfulness of aggregation functions
type: Item
instance of: scholarly article
title: On comparison meaningfulness of aggregation functions
zbMATH Open document ID: 1015.91058
author: Jean-Luc Marichal
author: Pierre Mathonet
published in: Journal of Mathematical Psychology
publication date: 2003-07-09T00:00:00Z
review text: An aggregation function is a function \(M: [a,b]^n\to \mathbb R\), with \([a,b]\) an interval of reals; it is assumed continuous. One may think of \(x^A\in[a,b]^n\) as the vector of values assigned to some outcome \(A\in{\mathcal A}\) by a group of \(n\) people -- \(x^A_i\) being the value of \(A\) for subject \(i\). \(M\) is comparison meaningful if the inequalities \(M(x)\geq M(x')\) are preserved under monotonic transformations of \(x,x'\); and idempotent if \(M(x,x,\dots,x)=x\); and symmetric if it is invariant under permutations. It is known that such aggregators are all equal to some order statistic, that is \(M(x)=x_{(k)}\) for some \(k\), with \(x_{(k)}\) being the \(k\)-th larger element of \(x\). The main result of the present paper is that if one drops idempotency, the non-constant \(M\)'s are increasing transformations of order statistics.
reviewed by: Salvatore Modica
Mathematics Subject Classification ID: 91C05
Mathematics Subject Classification ID: 28E10
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 91E45
zbMATH DE Number: 1750018
zbMATH Keywords: non-idempotent aggregators
MaRDI profile type: Publication
OpenAlex ID: W2014376081
Wikidata QID: Q52065867
cites work: On the possible merging functions
cites work: On scientific laws without dimensional constants
cites work: Q4315286
cites work: On the possible scientific laws
cites work: On Sugeno integral as an aggregation function
cites work: Means on ordered sets
cites work: Invariant functions on simple orders
cites work: Measurement Theory
cites work: Q5576064
DOI: 10.1006/JMPS.1999.1309
description: scientific article; zbMATH DE number 1750018