On the associativity functional equation
type: Item
instance of: scholarly article
title: On the associativity functional equation
zbMATH Open document ID: 0962.39012
DOI: 10.1016/S0165-0114(98)00332-7
author: Jean-Luc Marichal
published in: Fuzzy Sets and Systems
publication date: 2001-06-14T00:00:00Z
review text: The author describes the class of continuous, nondecreasing, associative functions \(M:[a,b]^2 \to[a,b]\) such that \(M(a,a)=a\) and \(M(b,b)=b\), where \([a,b]\) is a bounded closed real interval. To this end the author surveys many known results of J. Aczél, C. H. Ling, B. Schweizer, A. Sklar, J. C. Fodor, E. Czogala, J. Drewniak, P. S. Mostert and A. L. Shields. A new result is presented dealing with the class \(A_{a,b}\) of continuous, nondecreasing, associative functions \(M\) such that \(M(a,a)=a\) and \(M(b,b)=b\) and the subclass \(A_{a,b,c}\) where \(M(a,b)= M(b,a)=c\), \(c\in[a,b]\).
reviewed by: Claudi Alsina
Mathematics Subject Classification ID: 39B22
zbMATH DE Number: 1517317
zbMATH Keywords: associativity functional equation
zbMATH Keywords: continuous nondecreasing solutions
MaRDI profile type: Publication
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full work available at URL: s0165-0114(98)00332-7
OpenAlex ID: W2008695423
description: scientific article; zbMATH DE number 1517317