On weighted synthesis of judgements
type: Item
instance of: scholarly article
title: On weighted synthesis of judgements
zbMATH Open document ID: 0543.90003
DOI: 10.1007/BF02192678
author: János Aczél
published in: Aequationes Mathematicae
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137031
review text: The problems connected to synthesizing judgements [see the author and \textit{T. J. Saaty}, J. Math. Psychol. 27, 93-102 (1983; Zbl 0522.92028) and the author and \textit{C. Alsina}, Methods Oper. Res. 48, 3-22 (1984; Zbl 0527.39002)] are solved here in the nonsymmetric case where the synthesizing function is \(f(x_ 1,...,x_ n)=g_ 1(x_ 1)\circ...\circ g_ n(x_ n).\) The results are reasonably similar to the symmetric case and so are the conditions except that cancellativity is replaced by the local sensitivity (or partial philandering) property of f which states in this case that \(x_ k\mapsto f(x_ 1,...x_ k,...,x_ n)\) has no constant interval \((k=1,...,n)\).
Mathematics Subject Classification ID: 91B10
Mathematics Subject Classification ID: 90B50
Mathematics Subject Classification ID: 91E99
zbMATH DE Number: 3864919
zbMATH Keywords: weighted synthesis of judgements
zbMATH Keywords: unanimity
zbMATH Keywords: nonsymmetric case
zbMATH Keywords: synthesizing function
zbMATH Keywords: local sensitivity
MaRDI profile type: Publication
cites work: Q5735494
cites work: Q5514010
cites work: Extensions of certain homomorphisms of subsemigroups to homomorphisms of groups
cites work: Procedures for synthesizing ratio judgements
cites work: Simultaneous conjoint measurement: A new type of fundamental measurement
cites work: Q3714846
cites work: Q4105966
OpenAlex ID: W4251153866
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description: scientific article; zbMATH DE number 3864919