Lattice of fuzzy subalgebras and closure systems in \(I^ X\)
type: Item
instance of: scholarly article
title: Lattice of fuzzy subalgebras and closure systems in \(I^ X\)
zbMATH Open document ID: 0731.08007
DOI: 10.1016/0165-0114(91)90160-R
author: N. E. Zubov
published in: Fuzzy Sets and Systems
publication date: 1991-01-01T00:00:00Z
review text: For a given universal algebra \(A=[X,F]\) with a specified set F of finitary operations on the set X, each operation is extended to a finitary operation on the lattice \(I^ X\) of fuzzy subsets of X over the unit interval of real numbers \(I=[0,1]\). It is shown that the lattice of fuzzy subalgebras of A is an algebraic closure system in \(I^ X\) according to an appropriate definition.
Mathematics Subject Classification ID: 08A99
Mathematics Subject Classification ID: 06B99
zbMATH DE Number: 4208138
zbMATH Keywords: fuzzy algebra
zbMATH Keywords: fuzzy universal algebra
zbMATH Keywords: fuzzy closure system
zbMATH Keywords: fuzzy subalgebras
reviewed by: Vladimir V. Topentcharov
MaRDI profile type: Publication
cites work: Q5331549
cites work: Q5515373
cites work: Normalization of fuzzy algebras
cites work: Q5572358
cites work: Fuzzy vector spaces and fuzzy topological vector spaces
cites work: Fuzzy invariant subgroups and fuzzy ideals
cites work: Fuzzy groups
cites work: Q3898534
cites work: Fuzzy sets
cites work: The concept of a linguistic variable and its application to approximate reasoning. II
full work available at URL: 0165-0114(91)90160-r
OpenAlex ID: W1972260104
description: scientific article; zbMATH DE number 4208138