Vague Congruences and Quotient Lattice Implication Algebras

The aim of this paper is to further develop the congruence theory on lattice implication algebras. Firstly, we introduce the notions of vague similarity relations based on vague relations and vague congruence relations. Secondly, the equivalent characterizations of vague congruence relations are inv...

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Detalles Bibliográficos
Autores principales: Qin, Xiaoyan, Liu, Yi, Xu, Yang
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/PMC4123574/
https://www.ncbi.nlm.nih.gov/pubmed/25133207
http://dx.doi.org/10.1155/2014/197403
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author Qin, Xiaoyan
Liu, Yi
Xu, Yang
author_facet Qin, Xiaoyan
Liu, Yi
Xu, Yang
author_sort Qin, Xiaoyan
collection PubMed
description The aim of this paper is to further develop the congruence theory on lattice implication algebras. Firstly, we introduce the notions of vague similarity relations based on vague relations and vague congruence relations. Secondly, the equivalent characterizations of vague congruence relations are investigated. Thirdly, the relation between the set of vague filters and the set of vague congruences is studied. Finally, we construct a new lattice implication algebra induced by a vague congruence, and the homomorphism theorem is given.
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spelling pubmed-41235742014-08-17 Vague Congruences and Quotient Lattice Implication Algebras Qin, Xiaoyan Liu, Yi Xu, Yang ScientificWorldJournal Research Article The aim of this paper is to further develop the congruence theory on lattice implication algebras. Firstly, we introduce the notions of vague similarity relations based on vague relations and vague congruence relations. Secondly, the equivalent characterizations of vague congruence relations are investigated. Thirdly, the relation between the set of vague filters and the set of vague congruences is studied. Finally, we construct a new lattice implication algebra induced by a vague congruence, and the homomorphism theorem is given. Hindawi Publishing Corporation 2014 2014-07-14 /pmc/articles/PMC4123574/ /pubmed/25133207 http://dx.doi.org/10.1155/2014/197403 Text en Copyright © 2014 Xiaoyan Qin 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
Qin, Xiaoyan
Liu, Yi
Xu, Yang
Vague Congruences and Quotient Lattice Implication Algebras
title Vague Congruences and Quotient Lattice Implication Algebras
title_full Vague Congruences and Quotient Lattice Implication Algebras
title_fullStr Vague Congruences and Quotient Lattice Implication Algebras
title_full_unstemmed Vague Congruences and Quotient Lattice Implication Algebras
title_short Vague Congruences and Quotient Lattice Implication Algebras
title_sort vague congruences and quotient lattice implication algebras
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4123574/
https://www.ncbi.nlm.nih.gov/pubmed/25133207
http://dx.doi.org/10.1155/2014/197403
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AT liuyi vaguecongruencesandquotientlatticeimplicationalgebras
AT xuyang vaguecongruencesandquotientlatticeimplicationalgebras

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