Xor-Implications and E-implications: classes of fuzzy implications based on fuzzy Xor

Detalhes bibliográficos
Autor(a) principal: Bedregal, Benjamín Callejas
Data de Publicação: 2009
Outros Autores: Reiser, Renata Hax Sander, Dimuro, Graçaliz Pereira
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da FURG (RI FURG)
Texto Completo: http://repositorio.furg.br/handle/1/4683
Resumo: The main contribution of this paper is to introduce an autonomous definition of the connective “fuzzy exclusive or” (fuzzy Xor, for short), which is independent from others connectives. Also, two canonical definitions of the connective Xor are obtained from the composition of fuzzy connectives, and based on the commutative and associative properties related to the notions of triangular norms, triangular conorms and fuzzy negations. We show that the main properties of the classical connective Xor are preserved by the connective fuzzy Xor, and, therefore, this new definition of the connective fuzzy Xor extends the related classical approach. The definitions of fuzzy Xor-implications and fuzzy E-implications, induced by the fuzzy Xor connective, are also studied, and their main properties are analyzed. The relationships between the fuzzy Xor-implications and the fuzzy E-implications with automorphisms are explored.
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spelling Xor-Implications and E-implications: classes of fuzzy implications based on fuzzy XorFuzzy logicFuzzy xorXor-implicationE-ImplicationAutomorphismThe main contribution of this paper is to introduce an autonomous definition of the connective “fuzzy exclusive or” (fuzzy Xor, for short), which is independent from others connectives. Also, two canonical definitions of the connective Xor are obtained from the composition of fuzzy connectives, and based on the commutative and associative properties related to the notions of triangular norms, triangular conorms and fuzzy negations. We show that the main properties of the classical connective Xor are preserved by the connective fuzzy Xor, and, therefore, this new definition of the connective fuzzy Xor extends the related classical approach. The definitions of fuzzy Xor-implications and fuzzy E-implications, induced by the fuzzy Xor connective, are also studied, and their main properties are analyzed. The relationships between the fuzzy Xor-implications and the fuzzy E-implications with automorphisms are explored.2014-11-30T01:32:21Z2014-11-30T01:32:21Z2009info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfBEDREGAL, Benjamín Callejas; REISER, Renata Hax Sander; DIMURO, Graçaliz Pereira. Xor-Implications and E-implications: classes of fuzzy implications based on fuzzy Xor. Electronic Notes in Theoretical Computer Science, v. 247, p. 5-18, 2009. Disponível em: <http://ac.els-cdn.com/S1571066109002680/1-s2.0-S1571066109002680-main.pdf?_tid=e6541276-7199-11e4-8d9c-00000aacb361&acdnat=1416586833_3c6144934bffe162610cb65cfd71a4be>. Acesso em: 21 nov. 20141571-0661http://repositorio.furg.br/handle/1/468310.1016/j.entcs.2009.07.045engBedregal, Benjamín CallejasReiser, Renata Hax SanderDimuro, Graçaliz Pereirainfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da FURG (RI FURG)instname:Universidade Federal do Rio Grande (FURG)instacron:FURG2014-11-30T01:32:21Zoai:repositorio.furg.br:1/4683Repositório InstitucionalPUBhttps://repositorio.furg.br/oai/request || http://200.19.254.174/oai/requestopendoar:2014-11-30T01:32:21Repositório Institucional da FURG (RI FURG) - Universidade Federal do Rio Grande (FURG)false
dc.title.none.fl_str_mv Xor-Implications and E-implications: classes of fuzzy implications based on fuzzy Xor
title Xor-Implications and E-implications: classes of fuzzy implications based on fuzzy Xor
spellingShingle Xor-Implications and E-implications: classes of fuzzy implications based on fuzzy Xor
Bedregal, Benjamín Callejas
Fuzzy logic
Fuzzy xor
Xor-implication
E-Implication
Automorphism
title_short Xor-Implications and E-implications: classes of fuzzy implications based on fuzzy Xor
title_full Xor-Implications and E-implications: classes of fuzzy implications based on fuzzy Xor
title_fullStr Xor-Implications and E-implications: classes of fuzzy implications based on fuzzy Xor
title_full_unstemmed Xor-Implications and E-implications: classes of fuzzy implications based on fuzzy Xor
title_sort Xor-Implications and E-implications: classes of fuzzy implications based on fuzzy Xor
author Bedregal, Benjamín Callejas
author_facet Bedregal, Benjamín Callejas
Reiser, Renata Hax Sander
Dimuro, Graçaliz Pereira
author_role author
author2 Reiser, Renata Hax Sander
Dimuro, Graçaliz Pereira
author2_role author
author
dc.contributor.author.fl_str_mv Bedregal, Benjamín Callejas
Reiser, Renata Hax Sander
Dimuro, Graçaliz Pereira
dc.subject.por.fl_str_mv Fuzzy logic
Fuzzy xor
Xor-implication
E-Implication
Automorphism
topic Fuzzy logic
Fuzzy xor
Xor-implication
E-Implication
Automorphism
description The main contribution of this paper is to introduce an autonomous definition of the connective “fuzzy exclusive or” (fuzzy Xor, for short), which is independent from others connectives. Also, two canonical definitions of the connective Xor are obtained from the composition of fuzzy connectives, and based on the commutative and associative properties related to the notions of triangular norms, triangular conorms and fuzzy negations. We show that the main properties of the classical connective Xor are preserved by the connective fuzzy Xor, and, therefore, this new definition of the connective fuzzy Xor extends the related classical approach. The definitions of fuzzy Xor-implications and fuzzy E-implications, induced by the fuzzy Xor connective, are also studied, and their main properties are analyzed. The relationships between the fuzzy Xor-implications and the fuzzy E-implications with automorphisms are explored.
publishDate 2009
dc.date.none.fl_str_mv 2009
2014-11-30T01:32:21Z
2014-11-30T01:32:21Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv BEDREGAL, Benjamín Callejas; REISER, Renata Hax Sander; DIMURO, Graçaliz Pereira. Xor-Implications and E-implications: classes of fuzzy implications based on fuzzy Xor. Electronic Notes in Theoretical Computer Science, v. 247, p. 5-18, 2009. Disponível em: <http://ac.els-cdn.com/S1571066109002680/1-s2.0-S1571066109002680-main.pdf?_tid=e6541276-7199-11e4-8d9c-00000aacb361&acdnat=1416586833_3c6144934bffe162610cb65cfd71a4be>. Acesso em: 21 nov. 2014
1571-0661
http://repositorio.furg.br/handle/1/4683
10.1016/j.entcs.2009.07.045
identifier_str_mv BEDREGAL, Benjamín Callejas; REISER, Renata Hax Sander; DIMURO, Graçaliz Pereira. Xor-Implications and E-implications: classes of fuzzy implications based on fuzzy Xor. Electronic Notes in Theoretical Computer Science, v. 247, p. 5-18, 2009. Disponível em: <http://ac.els-cdn.com/S1571066109002680/1-s2.0-S1571066109002680-main.pdf?_tid=e6541276-7199-11e4-8d9c-00000aacb361&acdnat=1416586833_3c6144934bffe162610cb65cfd71a4be>. Acesso em: 21 nov. 2014
1571-0661
10.1016/j.entcs.2009.07.045
url http://repositorio.furg.br/handle/1/4683
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Institucional da FURG (RI FURG)
instname:Universidade Federal do Rio Grande (FURG)
instacron:FURG
instname_str Universidade Federal do Rio Grande (FURG)
instacron_str FURG
institution FURG
reponame_str Repositório Institucional da FURG (RI FURG)
collection Repositório Institucional da FURG (RI FURG)
repository.name.fl_str_mv Repositório Institucional da FURG (RI FURG) - Universidade Federal do Rio Grande (FURG)
repository.mail.fl_str_mv
_version_ 1807384400007004160

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