Decomposition and arrow-like aggregation of fuzzy preferences

We analyze the concept of a fuzzy preference on a set of alternatives, and how it can be decomposed in a triplet of new fuzzy binary relations that represent strict preference, weak preference and indifference. In this setting, we analyze the problem of aggregation of individual fuzzy preferences in...

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Autores: Raventós Pujol, Armajac, Campión Arrastia, María Jesús, Induráin Eraso, Esteban
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2020
País:España
Recursos:Universidad Pública de Navarra
Repositório:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/37331
Acesso em linha:https://hdl.handle.net/2454/37331
Access Level:Acceso aberto
Palavra-chave:Arrow’s impossibility theorems
Mathematical social choice
Fuzzy preferences
Decomposition of preferences
Aggregation of individual profiles
Social rules
Arrovian models, Paretian property
Independence of irrelevant alternatives
Dictatorship
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spelling Decomposition and arrow-like aggregation of fuzzy preferencesRaventós Pujol, ArmajacCampión Arrastia, María JesúsInduráin Eraso, EstebanArrow’s impossibility theoremsMathematical social choiceFuzzy preferencesDecomposition of preferencesAggregation of individual profilesSocial rulesArrovian models, Paretian propertyIndependence of irrelevant alternativesDictatorshipWe analyze the concept of a fuzzy preference on a set of alternatives, and how it can be decomposed in a triplet of new fuzzy binary relations that represent strict preference, weak preference and indifference. In this setting, we analyze the problem of aggregation of individual fuzzy preferences in a society into a global one that represents the whole society and accomplishes a shortlist of common-sense properties in the spirit of the Arrovian model for crisp preferences. We introduce a new technique that allows us to control a fuzzy preference by means of five crisp binary relations. This leads to an Arrovian impossibility theorem in this particular fuzzy setting.This work is partially supported by the research projects MTM2015-63608-P and TIN2016-77356-P (MINECO/ AEI-FEDER, UE).MDPIEstatistika, Informatika eta MatematikaInstitute for Advanced Research in Business and Economics - INARBEInstitute for Advanced Materials and Mathematics - INAMAT2Estadística, Informática y Matemáticas2020info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2454/37331reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarrainstname:Universidad Pública de NavarraInglésinfo:eu-repo/grantAgreement/MINECO//MTM2015-63608-Pinfo:eu-repo/grantAgreement/ES/1PE/TIN2016-77356-P© 2020 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:2454/373312026-06-17T12:41:47Z
dc.title.none.fl_str_mv Decomposition and arrow-like aggregation of fuzzy preferences
title Decomposition and arrow-like aggregation of fuzzy preferences
spellingShingle Decomposition and arrow-like aggregation of fuzzy preferences
Raventós Pujol, Armajac
Arrow’s impossibility theorems
Mathematical social choice
Fuzzy preferences
Decomposition of preferences
Aggregation of individual profiles
Social rules
Arrovian models, Paretian property
Independence of irrelevant alternatives
Dictatorship
title_short Decomposition and arrow-like aggregation of fuzzy preferences
title_full Decomposition and arrow-like aggregation of fuzzy preferences
title_fullStr Decomposition and arrow-like aggregation of fuzzy preferences
title_full_unstemmed Decomposition and arrow-like aggregation of fuzzy preferences
title_sort Decomposition and arrow-like aggregation of fuzzy preferences
dc.creator.none.fl_str_mv Raventós Pujol, Armajac
Campión Arrastia, María Jesús
Induráin Eraso, Esteban
author Raventós Pujol, Armajac
author_facet Raventós Pujol, Armajac
Campión Arrastia, María Jesús
Induráin Eraso, Esteban
author_role author
author2 Campión Arrastia, María Jesús
Induráin Eraso, Esteban
author2_role author
author
dc.contributor.none.fl_str_mv Estatistika, Informatika eta Matematika
Institute for Advanced Research in Business and Economics - INARBE
Institute for Advanced Materials and Mathematics - INAMAT2
Estadística, Informática y Matemáticas
dc.subject.none.fl_str_mv Arrow’s impossibility theorems
Mathematical social choice
Fuzzy preferences
Decomposition of preferences
Aggregation of individual profiles
Social rules
Arrovian models, Paretian property
Independence of irrelevant alternatives
Dictatorship
topic Arrow’s impossibility theorems
Mathematical social choice
Fuzzy preferences
Decomposition of preferences
Aggregation of individual profiles
Social rules
Arrovian models, Paretian property
Independence of irrelevant alternatives
Dictatorship
description We analyze the concept of a fuzzy preference on a set of alternatives, and how it can be decomposed in a triplet of new fuzzy binary relations that represent strict preference, weak preference and indifference. In this setting, we analyze the problem of aggregation of individual fuzzy preferences in a society into a global one that represents the whole society and accomplishes a shortlist of common-sense properties in the spirit of the Arrovian model for crisp preferences. We introduce a new technique that allows us to control a fuzzy preference by means of five crisp binary relations. This leads to an Arrovian impossibility theorem in this particular fuzzy setting.
publishDate 2020
dc.date.none.fl_str_mv 2020
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/2454/37331
url https://hdl.handle.net/2454/37331
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/MINECO//MTM2015-63608-P
info:eu-repo/grantAgreement/ES/1PE/TIN2016-77356-P
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
repository.name.fl_str_mv
repository.mail.fl_str_mv
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