Xor-Implications and E-implications: classes of fuzzy implications based on fuzzy Xor
Autor(a) principal: | |
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Data de Publicação: | 2009 |
Outros Autores: | , |
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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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 |
|
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1807384400007004160 |