Fuzzy maximal ideals of BCI and MV algebras
type: Item
instance of: scholarly article
title: Fuzzy maximal ideals of BCI and MV algebras
zbMATH Open document ID: 0809.06012
DOI: 10.1016/0020-0255(94)90081-7
published in: Information Sciences
publication date: 1994-11-23T00:00:00Z
review text: Let \(X\) be a BCI-algebra and let \(F(X)\) be the set of all fuzzy ideals of \(X\) which have 0 as a value. Then a fuzzy ideal of \(X\) is fuzzy maximal if it is nonconstant and its normalization is a maximal element of \(F(X)\) under an obvious partial ordering. It is then shown that such a fuzzy ideal is normalized and takes on only the values 0, 1. Relations are established between ideals and fuzzy ideals, and fuzzy maximal and fuzzy prime ideals for MV-algebras. Finally, an explicit construction is given for fuzzy ideals in such algebras which are not constants and are not characteristic functions of ideals.
Mathematics Subject Classification ID: 06F35
Mathematics Subject Classification ID: 06D30
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 694934
zbMATH Keywords: BCI-algebra
zbMATH Keywords: fuzzy ideals
zbMATH Keywords: MV-algebras
author: C. S. Hoo
author: Salvatore Sessa
reviewed by: C. S. Hoo
MaRDI profile type: Publication
full work available at URL: 0020-0255(94)90081-7
OpenAlex ID: W1980673059
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description: scientific article; zbMATH DE number 694934