On fuzzy ideals in BCK/BCI-algebras
type: Item
instance of: scholarly article
title: On fuzzy ideals in BCK/BCI-algebras
zbMATH Open document ID: 1070.06010
author: J. Meng
author: Xiu-é Guo
published in: Fuzzy Sets and Systems
publication date: 2005-01-31T00:00:00Z
review text: For BCI- and BCK-algebras, the authors define the notion of a fuzzy ideal generated by a fuzzy set. They then show that for a BCI-algebra, the set of all fuzzy ideals forms a complete lattice in an obvious way, and the set of closed fuzzy ideals is a modular sublattice of it. Some comments are made in the BCK-algebra case. This reviewer observes that the definition implies that for a BCK-algebra with largest element 1, if \(f\) is a fuzzy set with maximal value at 1, then the fuzzy ideal generated by it is constant with value \(f(1)\).
reviewed by: C. S. Hoo
Mathematics Subject Classification ID: 06F35
zbMATH DE Number: 2131588
zbMATH Keywords: BCI-algebra
zbMATH Keywords: BCK-algebra
zbMATH Keywords: fuzzy ideal
MaRDI profile type: Publication
full work available at URL: j.fss.2003.11.014
OpenAlex ID: W1999225201
cites work: Q4275496
cites work: Q4168924
cites work: Algebraic Analysis of Many Valued Logics
cites work: A New Proof of the Completeness of the Lukasiewicz Axioms
cites work: Fuzzy groups and level subgroups
cites work: Q5202228
cites work: Q3872458
cites work: Q4126337
cites work: Q4165379
cites work: Fuzzy commutative ideals of BCK-algebras
cites work: Characterizations of Noetherian BCK-algebras via fuzzy ideals
cites work: Q4324470
cites work: Q4835100
cites work: Q4308665
cites work: Q4332273
cites work: Q4396499
cites work: Q4258147
cites work: Fuzzy implicative ideals of BCK-algebras
cites work: Quotient BCK-algebra induced by a fuzzy ideal
cites work: Q3770539
cites work: Q3914983
cites work: Q3323949
cites work: Fuzzy groups
cites work: Q3988760
cites work: Fuzzy sets
DOI: 10.1016/J.FSS.2003.11.014
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description: scientific article; zbMATH DE number 2131588