On BL-Algebras and its Interval Counterpart

Detalhes bibliográficos
Autor(a) principal: PAIVA,R.
Data de Publicação: 2019
Outros Autores: SANTIAGO,R., BEDREGAL,B.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512019000200241
Resumo: ABSTRACT Interval Fuzzy Logic and Interval-valued Fuzzy Sets have been widely investigated. Some Fuzzy Logics were algebraically modeled by Peter Hájek as BL-algebras. What is the algebraic counterpart for the interval setting? It is known from the literature that there is an incompatibility between some algebraic structures and its interval counterpart. This paper shows that such incompatibility is also present in the level of BL-algebras. Here we show both: (1) the impossibility of match imprecision and the correctness of the underlying BL-implication and (2) some facts about the intervalization of BL-algebras.
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spelling On BL-Algebras and its Interval CounterpartFuzzy LogicBL-Algebrasintervalscorrectness principleABSTRACT Interval Fuzzy Logic and Interval-valued Fuzzy Sets have been widely investigated. Some Fuzzy Logics were algebraically modeled by Peter Hájek as BL-algebras. What is the algebraic counterpart for the interval setting? It is known from the literature that there is an incompatibility between some algebraic structures and its interval counterpart. This paper shows that such incompatibility is also present in the level of BL-algebras. Here we show both: (1) the impossibility of match imprecision and the correctness of the underlying BL-implication and (2) some facts about the intervalization of BL-algebras.Sociedade Brasileira de Matemática Aplicada e Computacional2019-08-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512019000200241TEMA (São Carlos) v.20 n.2 2019reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)instname:Sociedade Brasileira de Matemática Aplicada e Computacionalinstacron:SBMAC10.5540/tema.2019.020.02.0241info:eu-repo/semantics/openAccessPAIVA,R.SANTIAGO,R.BEDREGAL,B.eng2019-09-12T00:00:00Zoai:scielo:S2179-84512019000200241Revistahttp://www.scielo.br/temaPUBhttps://old.scielo.br/oai/scielo-oai.phpcastelo@icmc.usp.br2179-84511677-1966opendoar:2019-09-12T00:00TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacionalfalse
dc.title.none.fl_str_mv On BL-Algebras and its Interval Counterpart
title On BL-Algebras and its Interval Counterpart
spellingShingle On BL-Algebras and its Interval Counterpart
PAIVA,R.
Fuzzy Logic
BL-Algebras
intervals
correctness principle
title_short On BL-Algebras and its Interval Counterpart
title_full On BL-Algebras and its Interval Counterpart
title_fullStr On BL-Algebras and its Interval Counterpart
title_full_unstemmed On BL-Algebras and its Interval Counterpart
title_sort On BL-Algebras and its Interval Counterpart
author PAIVA,R.
author_facet PAIVA,R.
SANTIAGO,R.
BEDREGAL,B.
author_role author
author2 SANTIAGO,R.
BEDREGAL,B.
author2_role author
author
dc.contributor.author.fl_str_mv PAIVA,R.
SANTIAGO,R.
BEDREGAL,B.
dc.subject.por.fl_str_mv Fuzzy Logic
BL-Algebras
intervals
correctness principle
topic Fuzzy Logic
BL-Algebras
intervals
correctness principle
description ABSTRACT Interval Fuzzy Logic and Interval-valued Fuzzy Sets have been widely investigated. Some Fuzzy Logics were algebraically modeled by Peter Hájek as BL-algebras. What is the algebraic counterpart for the interval setting? It is known from the literature that there is an incompatibility between some algebraic structures and its interval counterpart. This paper shows that such incompatibility is also present in the level of BL-algebras. Here we show both: (1) the impossibility of match imprecision and the correctness of the underlying BL-implication and (2) some facts about the intervalization of BL-algebras.
publishDate 2019
dc.date.none.fl_str_mv 2019-08-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512019000200241
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512019000200241
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.5540/tema.2019.020.02.0241
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv TEMA (São Carlos) v.20 n.2 2019
reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
instname:Sociedade Brasileira de Matemática Aplicada e Computacional
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional
instacron_str SBMAC
institution SBMAC
reponame_str TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
collection TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
repository.name.fl_str_mv TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacional
repository.mail.fl_str_mv castelo@icmc.usp.br
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