A survey on the mathematical foundations of axiomatic entropy: representability and orderings

Different abstract versions of entropy, encountered in science, are interpreted in the light of numerical representations of several ordered structures, as total-preorders, interval-orders and semiorders. Intransitivities, other aspects of entropy as competitive systems, additivity, etc., are also v...

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Autores: Campión Arrastia, María Jesús, Gómez Polo, Cristina, Induráin Eraso, Esteban, Raventós Pujol, Armajac
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2018
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:2454/38814
Acesso em linha:https://hdl.handle.net/2454/38814
Access Level:Acceso aberto
Palavra-chave:Ordered structures
Numerical representations
Entropy
Representability
Utility functions
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spelling A survey on the mathematical foundations of axiomatic entropy: representability and orderingsCampión Arrastia, María JesúsGómez Polo, CristinaInduráin Eraso, EstebanRaventós Pujol, ArmajacOrdered structuresNumerical representationsEntropyRepresentabilityUtility functionsDifferent abstract versions of entropy, encountered in science, are interpreted in the light of numerical representations of several ordered structures, as total-preorders, interval-orders and semiorders. Intransitivities, other aspects of entropy as competitive systems, additivity, etc., are also viewed in terms of representability of algebraic structures endowed with some compatible ordering. A particular attention is paid to the problem of the construction of an entropy function or their mathematical equivalents. Multidisciplinary comparisons to other similar frameworks are also discussed, pointing out the mathematical foundations.This work was partially supported by the research projects ECO2015-65031-R, MTM2015-63608-P (MINECO/AEI-FEDER, UE), 0011-1365-2016-000060, PC003-004-005 DRUG-MAG, TIN2016-77356-P (MINECO/AEI-FEDER, UE) and 0011-1365-2017-000118.MDPIEstatistika, Informatika eta MatematikaZientziakInstitute for Advanced Research in Business and Economics - INARBEInstitute for Advanced Materials and Mathematics - INAMAT2Estadística, Informática y MatemáticasCiencias2018info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2454/38814reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarrainstname:Universidad Pública de NavarraInglésinfo:eu-repo/grantAgreement/MINECO//ECO2015-65031-Rinfo:eu-repo/grantAgreement/MINECO//MTM2015-63608-Pinfo:eu-repo/grantAgreement/ES/1PE/TIN2016-77356-P© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access_x000D_ article distributed under the terms and conditions of the Creative Commons Attribution_x000D_ (CC BY) license.https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:academica-e.unavarra.es:2454/388142026-06-17T12:41:47Z
dc.title.none.fl_str_mv A survey on the mathematical foundations of axiomatic entropy: representability and orderings
title A survey on the mathematical foundations of axiomatic entropy: representability and orderings
spellingShingle A survey on the mathematical foundations of axiomatic entropy: representability and orderings
Campión Arrastia, María Jesús
Ordered structures
Numerical representations
Entropy
Representability
Utility functions
title_short A survey on the mathematical foundations of axiomatic entropy: representability and orderings
title_full A survey on the mathematical foundations of axiomatic entropy: representability and orderings
title_fullStr A survey on the mathematical foundations of axiomatic entropy: representability and orderings
title_full_unstemmed A survey on the mathematical foundations of axiomatic entropy: representability and orderings
title_sort A survey on the mathematical foundations of axiomatic entropy: representability and orderings
dc.creator.none.fl_str_mv Campión Arrastia, María Jesús
Gómez Polo, Cristina
Induráin Eraso, Esteban
Raventós Pujol, Armajac
author Campión Arrastia, María Jesús
author_facet Campión Arrastia, María Jesús
Gómez Polo, Cristina
Induráin Eraso, Esteban
Raventós Pujol, Armajac
author_role author
author2 Gómez Polo, Cristina
Induráin Eraso, Esteban
Raventós Pujol, Armajac
author2_role author
author
author
dc.contributor.none.fl_str_mv Estatistika, Informatika eta Matematika
Zientziak
Institute for Advanced Research in Business and Economics - INARBE
Institute for Advanced Materials and Mathematics - INAMAT2
Estadística, Informática y Matemáticas
Ciencias
dc.subject.none.fl_str_mv Ordered structures
Numerical representations
Entropy
Representability
Utility functions
topic Ordered structures
Numerical representations
Entropy
Representability
Utility functions
description Different abstract versions of entropy, encountered in science, are interpreted in the light of numerical representations of several ordered structures, as total-preorders, interval-orders and semiorders. Intransitivities, other aspects of entropy as competitive systems, additivity, etc., are also viewed in terms of representability of algebraic structures endowed with some compatible ordering. A particular attention is paid to the problem of the construction of an entropy function or their mathematical equivalents. Multidisciplinary comparisons to other similar frameworks are also discussed, pointing out the mathematical foundations.
publishDate 2018
dc.date.none.fl_str_mv 2018
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/2454/38814
url https://hdl.handle.net/2454/38814
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
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info:eu-repo/grantAgreement/MINECO//MTM2015-63608-P
info:eu-repo/grantAgreement/ES/1PE/TIN2016-77356-P
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