On Fuzzy Implication Functions Based on Admissible Orders on the Set of Discrete Fuzzy Numbers

Research on the construction of logical connectives using total (admissible) orders is a prolific area of study. Using such orders, a new method for constructing implication functions is defined on the set of discrete fuzzy numbers with support of a closed interval of a given finite chain and whose...

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Detalles Bibliográficos
Autores: González-Hidalgo, Manuel, Massanet, Sebastia, Mir Torres, Arnau, Riera, Juan Vicente, De Miguel, Laura
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Conselleria de Salut i Consum del Govern de les Illes Balears
Repositorio:Docusalut
Idioma:inglés
OAI Identifier:oai:docusalut.com:20.500.13003/26044
Acceso en línea:https://hdl.handle.net/20.500.13003/26044
Access Level:acceso abierto
Palabra clave:Mathematics
Fuzzy Logic
Matemática
Lógica Difusa
Construction method
Discrete fuzzy numbers
Finite chains
Finite set
Fuzzy implications
Implication functions
Logical connectives
Membership values
Property
Total ordering
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spelling On Fuzzy Implication Functions Based on Admissible Orders on the Set of Discrete Fuzzy NumbersGonzález-Hidalgo, ManuelMassanet, SebastiaMir Torres, ArnauRiera, Juan VicenteDe Miguel, LauraMathematicsFuzzy LogicMatemáticaLógica DifusaConstruction methodDiscrete fuzzy numbersFinite chainsFinite setFuzzy implicationsImplication functionsLogical connectivesMembership valuesPropertyTotal orderingResearch on the construction of logical connectives using total (admissible) orders is a prolific area of study. Using such orders, a new method for constructing implication functions is defined on the set of discrete fuzzy numbers with support of a closed interval of a given finite chain and whose membership values belong to a finite set of fixed values. This method is based on the use of discrete implication functions defined on a finite chain. Furthermore, a bijective correspondence between the set of implication functions on the aforementioned subset of discrete fuzzy numbers and the set of discrete implication functions defined on the discrete chain is shown. Basic properties of these implication functions are thoroughly investigated, concluding that they are preserved under the proposed construction method. This result highlights the robustness and generality of the method, providing a systematic way to extend discrete implication functions to more complex structures while preserving their underlying properties. © The Author(s) 2025.Springer Science and Business Media LLC20252025-06-0220252025-06-02research articlehttp://purl.org/coar/resource_type/c_2df8fbb1info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.13003/26044reponame:Docusalutinstname:Conselleria de Salut i Consum del Govern de les Illes BalearsInglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:docusalut.com:20.500.13003/260442026-06-22T12:44:07Z
dc.title.none.fl_str_mv On Fuzzy Implication Functions Based on Admissible Orders on the Set of Discrete Fuzzy Numbers
title On Fuzzy Implication Functions Based on Admissible Orders on the Set of Discrete Fuzzy Numbers
spellingShingle On Fuzzy Implication Functions Based on Admissible Orders on the Set of Discrete Fuzzy Numbers
González-Hidalgo, Manuel
Mathematics
Fuzzy Logic
Matemática
Lógica Difusa
Construction method
Discrete fuzzy numbers
Finite chains
Finite set
Fuzzy implications
Implication functions
Logical connectives
Membership values
Property
Total ordering
title_short On Fuzzy Implication Functions Based on Admissible Orders on the Set of Discrete Fuzzy Numbers
title_full On Fuzzy Implication Functions Based on Admissible Orders on the Set of Discrete Fuzzy Numbers
title_fullStr On Fuzzy Implication Functions Based on Admissible Orders on the Set of Discrete Fuzzy Numbers
title_full_unstemmed On Fuzzy Implication Functions Based on Admissible Orders on the Set of Discrete Fuzzy Numbers
title_sort On Fuzzy Implication Functions Based on Admissible Orders on the Set of Discrete Fuzzy Numbers
dc.creator.none.fl_str_mv González-Hidalgo, Manuel
Massanet, Sebastia
Mir Torres, Arnau
Riera, Juan Vicente
De Miguel, Laura
author González-Hidalgo, Manuel
author_facet González-Hidalgo, Manuel
Massanet, Sebastia
Mir Torres, Arnau
Riera, Juan Vicente
De Miguel, Laura
author_role author
author2 Massanet, Sebastia
Mir Torres, Arnau
Riera, Juan Vicente
De Miguel, Laura
author2_role author
author
author
author
dc.contributor.none.fl_str_mv
dc.subject.none.fl_str_mv Mathematics
Fuzzy Logic
Matemática
Lógica Difusa
Construction method
Discrete fuzzy numbers
Finite chains
Finite set
Fuzzy implications
Implication functions
Logical connectives
Membership values
Property
Total ordering
topic Mathematics
Fuzzy Logic
Matemática
Lógica Difusa
Construction method
Discrete fuzzy numbers
Finite chains
Finite set
Fuzzy implications
Implication functions
Logical connectives
Membership values
Property
Total ordering
description Research on the construction of logical connectives using total (admissible) orders is a prolific area of study. Using such orders, a new method for constructing implication functions is defined on the set of discrete fuzzy numbers with support of a closed interval of a given finite chain and whose membership values belong to a finite set of fixed values. This method is based on the use of discrete implication functions defined on a finite chain. Furthermore, a bijective correspondence between the set of implication functions on the aforementioned subset of discrete fuzzy numbers and the set of discrete implication functions defined on the discrete chain is shown. Basic properties of these implication functions are thoroughly investigated, concluding that they are preserved under the proposed construction method. This result highlights the robustness and generality of the method, providing a systematic way to extend discrete implication functions to more complex structures while preserving their underlying properties. © The Author(s) 2025.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-06-02
2025
2025-06-02
dc.type.none.fl_str_mv research article
http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.13003/26044
url https://hdl.handle.net/20.500.13003/26044
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer Science and Business Media LLC
publisher.none.fl_str_mv Springer Science and Business Media LLC
dc.source.none.fl_str_mv reponame:Docusalut
instname:Conselleria de Salut i Consum del Govern de les Illes Balears
instname_str Conselleria de Salut i Consum del Govern de les Illes Balears
reponame_str Docusalut
collection Docusalut
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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