Extensions of orders to a power set vs. scores of hesitant fuzzy elements: points in common of two parallel theories

We deal with two apparently disparate theories. One of them studies extensions of orderings from a set to its power set. The other one defines suitable scores on hesitant fuzzy elements. We show that both theories have the same mathematical substrate. Thus, important possibility/impossibility result...

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Autores: Induráin Eraso, Esteban, Munárriz Iriarte, Ana, Sara Goyen, Martín Sergio
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:España
Institución:Universidad Pública de Navarra
Repositorio:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/52496
Acceso en línea:https://hdl.handle.net/2454/52496
Access Level:acceso abierto
Palabra clave:Extensions of orders from a set to its power set
Criteria of extensions of orderings
Possibility and impossibility results
Hesitant fuzzy elements and sets
Scores
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spelling Extensions of orders to a power set vs. scores of hesitant fuzzy elements: points in common of two parallel theoriesInduráin Eraso, EstebanMunárriz Iriarte, AnaSara Goyen, Martín SergioExtensions of orders from a set to its power setCriteria of extensions of orderingsPossibility and impossibility resultsHesitant fuzzy elements and setsScoresWe deal with two apparently disparate theories. One of them studies extensions of orderings from a set to its power set. The other one defines suitable scores on hesitant fuzzy elements. We show that both theories have the same mathematical substrate. Thus, important possibility/impossibility results concerning criteria for extensions can be transferred to new results on scores. And conversely, conditions imposed a priori on scores can give rise to new extension criteria. This enhances and enriches both theories. We show examples of translations of classical results on extensions in the context of scores. Also, we state new results concerning the impossibility of finding a utility function representing some kind of extension order if some restrictions are imposed on the utility function considered as a score.This work was supported by the project of reference PID2022-136627NB-I00 from MCIN/AEI/10.13039/501100011033/FEDER, UE, and by ERDF A way of making Europe.MDPIEstadística, Informática y MatemáticasEstatistika, Informatika eta MatematikaInstitute for Advanced Research in Business and Economics - INARBEInstitute for Advanced Materials and Mathematics - INAMAT22024info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2454/52496reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarrainstname:Universidad Pública de NavarraInglésinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-136627NB-I00© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:academica-e.unavarra.es:2454/524962026-06-17T12:41:47Z
dc.title.none.fl_str_mv Extensions of orders to a power set vs. scores of hesitant fuzzy elements: points in common of two parallel theories
title Extensions of orders to a power set vs. scores of hesitant fuzzy elements: points in common of two parallel theories
spellingShingle Extensions of orders to a power set vs. scores of hesitant fuzzy elements: points in common of two parallel theories
Induráin Eraso, Esteban
Extensions of orders from a set to its power set
Criteria of extensions of orderings
Possibility and impossibility results
Hesitant fuzzy elements and sets
Scores
title_short Extensions of orders to a power set vs. scores of hesitant fuzzy elements: points in common of two parallel theories
title_full Extensions of orders to a power set vs. scores of hesitant fuzzy elements: points in common of two parallel theories
title_fullStr Extensions of orders to a power set vs. scores of hesitant fuzzy elements: points in common of two parallel theories
title_full_unstemmed Extensions of orders to a power set vs. scores of hesitant fuzzy elements: points in common of two parallel theories
title_sort Extensions of orders to a power set vs. scores of hesitant fuzzy elements: points in common of two parallel theories
dc.creator.none.fl_str_mv Induráin Eraso, Esteban
Munárriz Iriarte, Ana
Sara Goyen, Martín Sergio
author Induráin Eraso, Esteban
author_facet Induráin Eraso, Esteban
Munárriz Iriarte, Ana
Sara Goyen, Martín Sergio
author_role author
author2 Munárriz Iriarte, Ana
Sara Goyen, Martín Sergio
author2_role author
author
dc.contributor.none.fl_str_mv Estadística, Informática y Matemáticas
Estatistika, Informatika eta Matematika
Institute for Advanced Research in Business and Economics - INARBE
Institute for Advanced Materials and Mathematics - INAMAT2
dc.subject.none.fl_str_mv Extensions of orders from a set to its power set
Criteria of extensions of orderings
Possibility and impossibility results
Hesitant fuzzy elements and sets
Scores
topic Extensions of orders from a set to its power set
Criteria of extensions of orderings
Possibility and impossibility results
Hesitant fuzzy elements and sets
Scores
description We deal with two apparently disparate theories. One of them studies extensions of orderings from a set to its power set. The other one defines suitable scores on hesitant fuzzy elements. We show that both theories have the same mathematical substrate. Thus, important possibility/impossibility results concerning criteria for extensions can be transferred to new results on scores. And conversely, conditions imposed a priori on scores can give rise to new extension criteria. This enhances and enriches both theories. We show examples of translations of classical results on extensions in the context of scores. Also, we state new results concerning the impossibility of finding a utility function representing some kind of extension order if some restrictions are imposed on the utility function considered as a score.
publishDate 2024
dc.date.none.fl_str_mv 2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2454/52496
url https://hdl.handle.net/2454/52496
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-136627NB-I00
dc.rights.none.fl_str_mv https://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv https://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 MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
instname:Universidad Pública de Navarra
instname_str Universidad Pública de Navarra
reponame_str Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
collection Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
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repository.mail.fl_str_mv
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