(Fuzzy) Ideals of BN-Algebras

The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between...

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Detalles Bibliográficos
Autores principales: Dymek, Grzegorz, Walendziak, Andrzej
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2015
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4466498/
https://www.ncbi.nlm.nih.gov/pubmed/26125050
http://dx.doi.org/10.1155/2015/925040
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author Dymek, Grzegorz
Walendziak, Andrzej
author_facet Dymek, Grzegorz
Walendziak, Andrzej
author_sort Dymek, Grzegorz
collection PubMed
description The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given. The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are obtained.
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spelling pubmed-44664982015-06-29 (Fuzzy) Ideals of BN-Algebras Dymek, Grzegorz Walendziak, Andrzej ScientificWorldJournal Research Article The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given. The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are obtained. Hindawi Publishing Corporation 2015 2015-06-01 /pmc/articles/PMC4466498/ /pubmed/26125050 http://dx.doi.org/10.1155/2015/925040 Text en Copyright © 2015 G. Dymek and A. Walendziak. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Dymek, Grzegorz
Walendziak, Andrzej
(Fuzzy) Ideals of BN-Algebras
title (Fuzzy) Ideals of BN-Algebras
title_full (Fuzzy) Ideals of BN-Algebras
title_fullStr (Fuzzy) Ideals of BN-Algebras
title_full_unstemmed (Fuzzy) Ideals of BN-Algebras
title_short (Fuzzy) Ideals of BN-Algebras
title_sort (fuzzy) ideals of bn-algebras
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4466498/
https://www.ncbi.nlm.nih.gov/pubmed/26125050
http://dx.doi.org/10.1155/2015/925040
work_keys_str_mv AT dymekgrzegorz fuzzyidealsofbnalgebras
AT walendziakandrzej fuzzyidealsofbnalgebras

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