Characterizations of MV-Algebras Based on the Theory of Falling Shadows

Based on the falling shadow theory, the concept of falling fuzzy (implicative) ideals as a generalization of that of a T (∧)-fuzzy (implicative) ideal is proposed in MV-algebras. The relationships between falling fuzzy (implicative) ideals and T-fuzzy (implicative) ideals are discussed, and conditio...

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Detalles Bibliográficos
Autores principales: Yang, Yongwei, Xin, Xiaolong, He, Pengfei
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4167447/
https://www.ncbi.nlm.nih.gov/pubmed/25258743
http://dx.doi.org/10.1155/2014/951796
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author Yang, Yongwei
Xin, Xiaolong
He, Pengfei
author_facet Yang, Yongwei
Xin, Xiaolong
He, Pengfei
author_sort Yang, Yongwei
collection PubMed
description Based on the falling shadow theory, the concept of falling fuzzy (implicative) ideals as a generalization of that of a T (∧)-fuzzy (implicative) ideal is proposed in MV-algebras. The relationships between falling fuzzy (implicative) ideals and T-fuzzy (implicative) ideals are discussed, and conditions for a falling fuzzy (implicative) ideal to be a T (∧)-fuzzy (implicative) ideal are provided. Some characterizations of falling fuzzy (implicative) ideals are presented by studying proprieties of them. The product ⊛ and the up product ⊚ operations on falling shadows and the upset of a falling shadow are established, by which T-fuzzy ideals are investigated based on probability spaces.
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spelling pubmed-41674472014-09-25 Characterizations of MV-Algebras Based on the Theory of Falling Shadows Yang, Yongwei Xin, Xiaolong He, Pengfei ScientificWorldJournal Research Article Based on the falling shadow theory, the concept of falling fuzzy (implicative) ideals as a generalization of that of a T (∧)-fuzzy (implicative) ideal is proposed in MV-algebras. The relationships between falling fuzzy (implicative) ideals and T-fuzzy (implicative) ideals are discussed, and conditions for a falling fuzzy (implicative) ideal to be a T (∧)-fuzzy (implicative) ideal are provided. Some characterizations of falling fuzzy (implicative) ideals are presented by studying proprieties of them. The product ⊛ and the up product ⊚ operations on falling shadows and the upset of a falling shadow are established, by which T-fuzzy ideals are investigated based on probability spaces. Hindawi Publishing Corporation 2014 2014-08-28 /pmc/articles/PMC4167447/ /pubmed/25258743 http://dx.doi.org/10.1155/2014/951796 Text en Copyright © 2014 Yongwei Yang et al. 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
Yang, Yongwei
Xin, Xiaolong
He, Pengfei
Characterizations of MV-Algebras Based on the Theory of Falling Shadows
title Characterizations of MV-Algebras Based on the Theory of Falling Shadows
title_full Characterizations of MV-Algebras Based on the Theory of Falling Shadows
title_fullStr Characterizations of MV-Algebras Based on the Theory of Falling Shadows
title_full_unstemmed Characterizations of MV-Algebras Based on the Theory of Falling Shadows
title_short Characterizations of MV-Algebras Based on the Theory of Falling Shadows
title_sort characterizations of mv-algebras based on the theory of falling shadows
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4167447/
https://www.ncbi.nlm.nih.gov/pubmed/25258743
http://dx.doi.org/10.1155/2014/951796
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AT xinxiaolong characterizationsofmvalgebrasbasedonthetheoryoffallingshadows
AT hepengfei characterizationsofmvalgebrasbasedonthetheoryoffallingshadows

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