Addition and subtraction of interactive fuzzy numbers via family of joint possibility distributions

Detalhes bibliográficos
Autor(a) principal: Esmi, Estevão
Data de Publicação: 2021
Outros Autores: Wasques, Vinícius Francisco [UNESP], Carvalho de Barros, Laécio
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1016/j.fss.2021.03.005
http://hdl.handle.net/11449/221712
Resumo: In this article we propose a method to calculate the sum and difference of two interactive fuzzy numbers. These arithmetic operations are obtained by the sup-J extension principle, which is a generalization of the Zadeh's extension principle. We show that the proposed addition and subtraction produce fuzzy numbers with smaller width and norm than any other addition and subtraction for fuzzy numbers, obtained by joint possibility distributions. Moreover, we provide a characterization of these operations by means of α-cuts. We compare the proposed interactive addition with the standard one. We also establish connections among the proposed subtraction and the Hukuhara, generalized Hukuhara and generalize differences. Finally, we provide an application in the Malthusian Model in order to illustrate the results.
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spelling Addition and subtraction of interactive fuzzy numbers via family of joint possibility distributionsFuzzy arithmeticInteractive fuzzy numbersSup-J extension principleIn this article we propose a method to calculate the sum and difference of two interactive fuzzy numbers. These arithmetic operations are obtained by the sup-J extension principle, which is a generalization of the Zadeh's extension principle. We show that the proposed addition and subtraction produce fuzzy numbers with smaller width and norm than any other addition and subtraction for fuzzy numbers, obtained by joint possibility distributions. Moreover, we provide a characterization of these operations by means of α-cuts. We compare the proposed interactive addition with the standard one. We also establish connections among the proposed subtraction and the Hukuhara, generalized Hukuhara and generalize differences. Finally, we provide an application in the Malthusian Model in order to illustrate the results.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)University of Campinas Department of Applied MathematicsSão Paulo State University Department of MathematicsNational Center for Research in Energy and Materials Department of Integrated Science Teaching CenterSão Paulo State University Department of MathematicsCNPq: 142414/2017-4CNPq: 306546/2017-5FAPESP: 313313/2020-2Universidade Estadual de Campinas (UNICAMP)Universidade Estadual Paulista (UNESP)National Center for Research in Energy and MaterialsEsmi, EstevãoWasques, Vinícius Francisco [UNESP]Carvalho de Barros, Laécio2022-04-28T19:30:20Z2022-04-28T19:30:20Z2021-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1016/j.fss.2021.03.005Fuzzy Sets and Systems.0165-0114http://hdl.handle.net/11449/22171210.1016/j.fss.2021.03.0052-s2.0-85103551585Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengFuzzy Sets and Systemsinfo:eu-repo/semantics/openAccess2022-04-28T19:30:20Zoai:repositorio.unesp.br:11449/221712Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T16:35:28.304784Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Addition and subtraction of interactive fuzzy numbers via family of joint possibility distributions
title Addition and subtraction of interactive fuzzy numbers via family of joint possibility distributions
spellingShingle Addition and subtraction of interactive fuzzy numbers via family of joint possibility distributions
Esmi, Estevão
Fuzzy arithmetic
Interactive fuzzy numbers
Sup-J extension principle
title_short Addition and subtraction of interactive fuzzy numbers via family of joint possibility distributions
title_full Addition and subtraction of interactive fuzzy numbers via family of joint possibility distributions
title_fullStr Addition and subtraction of interactive fuzzy numbers via family of joint possibility distributions
title_full_unstemmed Addition and subtraction of interactive fuzzy numbers via family of joint possibility distributions
title_sort Addition and subtraction of interactive fuzzy numbers via family of joint possibility distributions
author Esmi, Estevão
author_facet Esmi, Estevão
Wasques, Vinícius Francisco [UNESP]
Carvalho de Barros, Laécio
author_role author
author2 Wasques, Vinícius Francisco [UNESP]
Carvalho de Barros, Laécio
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual de Campinas (UNICAMP)
Universidade Estadual Paulista (UNESP)
National Center for Research in Energy and Materials
dc.contributor.author.fl_str_mv Esmi, Estevão
Wasques, Vinícius Francisco [UNESP]
Carvalho de Barros, Laécio
dc.subject.por.fl_str_mv Fuzzy arithmetic
Interactive fuzzy numbers
Sup-J extension principle
topic Fuzzy arithmetic
Interactive fuzzy numbers
Sup-J extension principle
description In this article we propose a method to calculate the sum and difference of two interactive fuzzy numbers. These arithmetic operations are obtained by the sup-J extension principle, which is a generalization of the Zadeh's extension principle. We show that the proposed addition and subtraction produce fuzzy numbers with smaller width and norm than any other addition and subtraction for fuzzy numbers, obtained by joint possibility distributions. Moreover, we provide a characterization of these operations by means of α-cuts. We compare the proposed interactive addition with the standard one. We also establish connections among the proposed subtraction and the Hukuhara, generalized Hukuhara and generalize differences. Finally, we provide an application in the Malthusian Model in order to illustrate the results.
publishDate 2021
dc.date.none.fl_str_mv 2021-01-01
2022-04-28T19:30:20Z
2022-04-28T19:30:20Z
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 http://dx.doi.org/10.1016/j.fss.2021.03.005
Fuzzy Sets and Systems.
0165-0114
http://hdl.handle.net/11449/221712
10.1016/j.fss.2021.03.005
2-s2.0-85103551585
url http://dx.doi.org/10.1016/j.fss.2021.03.005
http://hdl.handle.net/11449/221712
identifier_str_mv Fuzzy Sets and Systems.
0165-0114
10.1016/j.fss.2021.03.005
2-s2.0-85103551585
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Fuzzy Sets and Systems
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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
_version_ 1808128675193815040

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