Adapted Fuzzy Integral: An Application in the Finite Element Method
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Outros Autores: | , , |
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=S2179-84512018000100147 |
Resumo: | ABSTRACT In this paper we study and define an adapted fuzzy integral, based on the Sugeno integral. Moreover, we present a numerical integration formula which approximates the value of the adapted fuzzy integral. Thus, we prove that the Riemann integral and the adapted fuzzy integral are equivalent for power functions. Next, we apply the formula proposed in the numerical integration, required in the finite element method, to obtain a numerical solution of a boundary value problem for the one-dimensional Poisson equation. Finally, we observed better results of the approximate solution obtained in the example with the use of our formula when compared with the simple trapezoidal rule. |
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Adapted Fuzzy Integral: An Application in the Finite Element MethodFuzzy MeasureSugeno IntegralFinite Element MethodBoundary Value ProblemABSTRACT In this paper we study and define an adapted fuzzy integral, based on the Sugeno integral. Moreover, we present a numerical integration formula which approximates the value of the adapted fuzzy integral. Thus, we prove that the Riemann integral and the adapted fuzzy integral are equivalent for power functions. Next, we apply the formula proposed in the numerical integration, required in the finite element method, to obtain a numerical solution of a boundary value problem for the one-dimensional Poisson equation. Finally, we observed better results of the approximate solution obtained in the example with the use of our formula when compared with the simple trapezoidal rule.Sociedade Brasileira de Matemática Aplicada e Computacional2018-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000100147TEMA (São Carlos) v.19 n.1 2018reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)instname:Sociedade Brasileira de Matemática Aplicada e Computacionalinstacron:SBMAC10.5540/tema.2018.019.01.0147info:eu-repo/semantics/openAccessSÁNCHEZ,D.BASSANI,L.T.BARROS,L.C.ESMI,E.eng2018-05-24T00:00:00Zoai:scielo:S2179-84512018000100147Revistahttp://www.scielo.br/temaPUBhttps://old.scielo.br/oai/scielo-oai.phpcastelo@icmc.usp.br2179-84511677-1966opendoar:2018-05-24T00:00TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacionalfalse |
dc.title.none.fl_str_mv |
Adapted Fuzzy Integral: An Application in the Finite Element Method |
title |
Adapted Fuzzy Integral: An Application in the Finite Element Method |
spellingShingle |
Adapted Fuzzy Integral: An Application in the Finite Element Method SÁNCHEZ,D. Fuzzy Measure Sugeno Integral Finite Element Method Boundary Value Problem |
title_short |
Adapted Fuzzy Integral: An Application in the Finite Element Method |
title_full |
Adapted Fuzzy Integral: An Application in the Finite Element Method |
title_fullStr |
Adapted Fuzzy Integral: An Application in the Finite Element Method |
title_full_unstemmed |
Adapted Fuzzy Integral: An Application in the Finite Element Method |
title_sort |
Adapted Fuzzy Integral: An Application in the Finite Element Method |
author |
SÁNCHEZ,D. |
author_facet |
SÁNCHEZ,D. BASSANI,L.T. BARROS,L.C. ESMI,E. |
author_role |
author |
author2 |
BASSANI,L.T. BARROS,L.C. ESMI,E. |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
SÁNCHEZ,D. BASSANI,L.T. BARROS,L.C. ESMI,E. |
dc.subject.por.fl_str_mv |
Fuzzy Measure Sugeno Integral Finite Element Method Boundary Value Problem |
topic |
Fuzzy Measure Sugeno Integral Finite Element Method Boundary Value Problem |
description |
ABSTRACT In this paper we study and define an adapted fuzzy integral, based on the Sugeno integral. Moreover, we present a numerical integration formula which approximates the value of the adapted fuzzy integral. Thus, we prove that the Riemann integral and the adapted fuzzy integral are equivalent for power functions. Next, we apply the formula proposed in the numerical integration, required in the finite element method, to obtain a numerical solution of a boundary value problem for the one-dimensional Poisson equation. Finally, we observed better results of the approximate solution obtained in the example with the use of our formula when compared with the simple trapezoidal rule. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-01-01 |
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=S2179-84512018000100147 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000100147 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.5540/tema.2018.019.01.0147 |
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.19 n.1 2018 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 |
_version_ |
1752122220256165888 |