Irreducibility in algebraic fuzzy systems
type: Item
instance of: scholarly article
title: Irreducibility in algebraic fuzzy systems
zbMATH Open document ID: 0732.08003
DOI: 10.1016/0165-0114(91)90227-H
author: U. Maddana Swamy
author: D. Viswanadha Raju
published in: Fuzzy Sets and Systems
publication date: 1991-01-01T00:00:00Z
review text: A general theory of algebraic fuzzy systems has been developed by the authors in the paper reviewed above (see Zbl 0732.08002). This paper continues this work; the main results concern irreducibility in algebraic fuzzy systems. The authors propose an important notion, prime fuzzy \({\mathcal S}\)-subsets of a nonempty set X having truth values in a complete Brouwerian lattice L, which is determined by pairs (p,\(\alpha\)), where p is a prime element of \({\mathcal S}\) and \(\alpha\) is an irreducible element of L. The main result is that the space of all prime fuzzy \({\mathcal S}\)- subsets of X together with its hull-kernel topology is homeomorphic to the product of the spaces of prime elements of \({\mathcal S}\) and of irreducible elements of L, equipped with hull-kernel topologies.
Mathematics Subject Classification ID: 08A99
Mathematics Subject Classification ID: 94D05
Mathematics Subject Classification ID: 54A40
zbMATH DE Number: 4210217
zbMATH Keywords: algebraic fuzzy systems
zbMATH Keywords: irreducibility
zbMATH Keywords: prime fuzzy \({\mathcal S}\)-subsets
zbMATH Keywords: hull-kernel topology
zbMATH Keywords: prime elements
zbMATH Keywords: irreducible elements
zbMATH Keywords: hull-kernel topologies
reviewed by: Hongxing Li
MaRDI profile type: Publication
cites work: Q3934450
cites work: L-fuzzy sets
cites work: Q4165427
cites work: On fuzzy ideals of a ring. I
cites work: Topological representations of distributive lattices and Brouwerian logics
cites work: Fuzzy prime ideals of rings
cites work: Fuzzy ideals and congruences of lattices
cites work: Algebraic fuzzy systems
cites work: Fuzzy sets
full work available at URL: 0165-0114(91)90227-h
OpenAlex ID: W2172189282
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description: scientific article; zbMATH DE number 4210217