Numerical Solution for Fuzzy Partial Differential Equations with Interactive Fuzzy Boundary Conditions

Detalhes bibliográficos
Autor(a) principal: Wasques, Vinícius F. [UNESP]
Data de Publicação: 2022
Tipo de documento: Artigo de conferência
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1007/978-3-030-82099-2_44
http://hdl.handle.net/11449/222271
Resumo: This paper presents a numerical method to solve fuzzy partial differential equations, where the initial and boundary conditions are given by interactive fuzzy numbers. Interactivity is a relationship between fuzzy numbers that is associated with the notion of joint possibility distribution. From this approach, different solutions are presented to the fuzzy partial differential equation. In addition to the method, an algorithm is proposed to determine which of these solutions is most suitable for a given problem. The numerical solution is given by the finite difference method, adapted for the arithmetic operations of interactive fuzzy numbers. The method is applied to the heat equation, in order to illustrate the results.
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spelling Numerical Solution for Fuzzy Partial Differential Equations with Interactive Fuzzy Boundary ConditionsFuzzy numerical methodFuzzy partial differential equationHeat equationInteractive fuzzy numbersThis paper presents a numerical method to solve fuzzy partial differential equations, where the initial and boundary conditions are given by interactive fuzzy numbers. Interactivity is a relationship between fuzzy numbers that is associated with the notion of joint possibility distribution. From this approach, different solutions are presented to the fuzzy partial differential equation. In addition to the method, an algorithm is proposed to determine which of these solutions is most suitable for a given problem. The numerical solution is given by the finite difference method, adapted for the arithmetic operations of interactive fuzzy numbers. The method is applied to the heat equation, in order to illustrate the results.National Center for Research in Energy and Materials São Paulo State UniversityNational Center for Research in Energy and Materials São Paulo State UniversityUniversidade Estadual Paulista (UNESP)Wasques, Vinícius F. [UNESP]2022-04-28T19:43:39Z2022-04-28T19:43:39Z2022-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObject486-498http://dx.doi.org/10.1007/978-3-030-82099-2_44Lecture Notes in Networks and Systems, v. 258, p. 486-498.2367-33892367-3370http://hdl.handle.net/11449/22227110.1007/978-3-030-82099-2_442-s2.0-85113374988Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengLecture Notes in Networks and Systems232479info:eu-repo/semantics/openAccess2023-01-11T19:22:21Zoai:repositorio.unesp.br:11449/222271Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T20:30:26.694547Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Numerical Solution for Fuzzy Partial Differential Equations with Interactive Fuzzy Boundary Conditions
title Numerical Solution for Fuzzy Partial Differential Equations with Interactive Fuzzy Boundary Conditions
spellingShingle Numerical Solution for Fuzzy Partial Differential Equations with Interactive Fuzzy Boundary Conditions
Wasques, Vinícius F. [UNESP]
Fuzzy numerical method
Fuzzy partial differential equation
Heat equation
Interactive fuzzy numbers
title_short Numerical Solution for Fuzzy Partial Differential Equations with Interactive Fuzzy Boundary Conditions
title_full Numerical Solution for Fuzzy Partial Differential Equations with Interactive Fuzzy Boundary Conditions
title_fullStr Numerical Solution for Fuzzy Partial Differential Equations with Interactive Fuzzy Boundary Conditions
title_full_unstemmed Numerical Solution for Fuzzy Partial Differential Equations with Interactive Fuzzy Boundary Conditions
title_sort Numerical Solution for Fuzzy Partial Differential Equations with Interactive Fuzzy Boundary Conditions
author Wasques, Vinícius F. [UNESP]
author_facet Wasques, Vinícius F. [UNESP]
author_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Wasques, Vinícius F. [UNESP]
dc.subject.por.fl_str_mv Fuzzy numerical method
Fuzzy partial differential equation
Heat equation
Interactive fuzzy numbers
topic Fuzzy numerical method
Fuzzy partial differential equation
Heat equation
Interactive fuzzy numbers
description This paper presents a numerical method to solve fuzzy partial differential equations, where the initial and boundary conditions are given by interactive fuzzy numbers. Interactivity is a relationship between fuzzy numbers that is associated with the notion of joint possibility distribution. From this approach, different solutions are presented to the fuzzy partial differential equation. In addition to the method, an algorithm is proposed to determine which of these solutions is most suitable for a given problem. The numerical solution is given by the finite difference method, adapted for the arithmetic operations of interactive fuzzy numbers. The method is applied to the heat equation, in order to illustrate the results.
publishDate 2022
dc.date.none.fl_str_mv 2022-04-28T19:43:39Z
2022-04-28T19:43:39Z
2022-01-01
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/conferenceObject
format conferenceObject
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1007/978-3-030-82099-2_44
Lecture Notes in Networks and Systems, v. 258, p. 486-498.
2367-3389
2367-3370
http://hdl.handle.net/11449/222271
10.1007/978-3-030-82099-2_44
2-s2.0-85113374988
url http://dx.doi.org/10.1007/978-3-030-82099-2_44
http://hdl.handle.net/11449/222271
identifier_str_mv Lecture Notes in Networks and Systems, v. 258, p. 486-498.
2367-3389
2367-3370
10.1007/978-3-030-82099-2_44
2-s2.0-85113374988
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Lecture Notes in Networks and Systems
232479
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 486-498
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
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