On a functional equation characterizing two binary operations on the space of membership functions
type: Item
instance of: scholarly article
title: On a functional equation characterizing two binary operations on the space of membership functions
zbMATH Open document ID: 0681.39007
DOI: 10.1016/0165-0114(88)90077-2
author: Claudi Alsina
published in: Fuzzy Sets and Systems
publication date: 1988-01-01T00:00:00Z
review text: Let * and \(\Delta\) be continuous, abelian semi-group operations on the fuzzy subsets of X with the topology of pointwise convergence. Assume that 1 and 0 are the respective units and that the sections of the binary operations are non-decreasing. The author characterizes the solutions of the functional equation \[ A*B+A\Delta B=A+B \] in terms of families of t-norms and t-conorms discovered by \textit{M. J. Frank} [Aequationes Math. 19, 194-226 (1979; Zbl 0444.39003)].
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 4115187
zbMATH Keywords: space of membership functions
zbMATH Keywords: fuzzy subsets
zbMATH Keywords: topology of pointwise convergence
zbMATH Keywords: functional equation
zbMATH Keywords: t-norms
zbMATH Keywords: t-conorms
MaRDI profile type: Publication
full work available at URL: 0165-0114(88)90077-2
OpenAlex ID: W2024773810
cites work: Q3743748
cites work: On some logical connectives for fuzzy sets theory
cites work: On the analytic formalism of the theory of fuzzy sets
cites work: On the simultaneous associativity of F(x,y) and x+y-F(x,y)
cites work: Q3336431
cites work: A fuzzy-algorithmic approach to the definition of complex or imprecise concepts
description: scientific article; zbMATH DE number 4115187