Some representable De Morgan algebras
type: Item
instance of: scholarly article
title: Some representable De Morgan algebras
zbMATH Open document ID: 0563.06012
DOI: 10.1016/0022-247X(84)90094-5
author: Francesc Esteva
published in: Journal of Mathematical Analysis and Applications
publication date: 1984-01-01T00:00:00Z
review text: For a set X, let \(R=\{R_ x: x\in X\}\) be a family of bounded lattices \((R_ x,\bigwedge_ x,\bigvee_ x,1_ x,0_ x)\). A fuzzy subset of X is defined as a mapping \(A: X\to \cup_{x\in X}R_ x\). The set of fuzzy subsets of X is denoted by \(P_ R(X)\) and operations \(\cup\) and \(\cap\) are defined by \((A\cup B)(x)=A(x)\vee_ xB(x)\) and \((A\cap B)(x)=A(x)\wedge_ xB(x)\). The author studies representations of De Morgan algebras by bounded lattices of fuzzy sets \((P_ R(X),\cup,\cap)\) on which some kind of involution can be defined.
reviewed by: V. Yu. Meskhi
Mathematics Subject Classification ID: 06D30
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 3896996
zbMATH Keywords: bounded lattices
zbMATH Keywords: representations of De Morgan algebras
zbMATH Keywords: fuzzy sets
MaRDI profile type: Publication
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cites work: Fuzzy sets
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description: scientific article; zbMATH DE number 3896996