Characterizing competition ranks within a comprehensive family of position operators

Producción Científica

Detalles Bibliográficos
Autores: Martínez Panero, Miguel, García Lapresta, José Luis
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2025
País:España
Institución:Universidad de Valladolid
Repositorio:UVaDOC. Repositorio Documental de la Universidad de Valladolid
OAI Identifier:oai:uvadoc.uva.es:10324/79452
Acceso en línea:https://doi.org/10.1016/j.ejor.2025.10.030
https://uvadoc.uva.es/handle/10324/79452
Access Level:acceso abierto
Palabra clave:Preference learning
Linear orders
Weak orders
Positions
Ranks
12 Matemáticas
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spelling Characterizing competition ranks within a comprehensive family of position operatorsMartínez Panero, MiguelGarcía Lapresta, José LuisPreference learningLinear ordersWeak ordersPositionsRanks12 MatemáticasProducción CientíficaThere is only one way to assign positions to objects arranged in linear orders: following the sequence of natural numbers (1, 2, 3, 4, …). However, in weak orders, where ties arise, there are different possibilities to assign positions to tied objects. In this paper, we focus mainly on three relevant cases: the standard, modified, and fractional ranks. They are differentiated by the spaces that appear after, before, or on either side of the position values corresponding to the objects that are in a tie. For instance, if two objects are tied and are located immedi- ately below the top object, these ranks assign the positions (1, 2, 2, 4, …), (1, 3, 3, 4, …), and (1, 2.5, 2.5, 4, …), respectively. Collectively, and because of the common properties shown here, we call them “competition ranks”. In this paper, we characterize a parameterized family of position operators which includes the competition ranks. We also provide specific axiomatizations of each of them, taking into account the spaces in the sequence of as- signed position numbers. It is shown why the dense rank (1, 2, 2, 3, …), another position operator where gaps do not appear, is an essentially different approach. Furthermore, interesting duality relationships are revealed between the competition ranks and between the properties introduced to characterize them, which allow us to understand their internal logic and connections. Different examples, mainly from sports, bibliometrics, etc., illustrate the introduced conceptsMinisterio de Ciencia, Innovación y Universidades - MICIU/AEI/10.13039/501100011033 y FEDER (UE) ( project PID2021-122506NB-I00)Elsevier2025info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://doi.org/10.1016/j.ejor.2025.10.030https://uvadoc.uva.es/handle/10324/79452reponame:UVaDOC. Repositorio Documental de la Universidad de Valladolidinstname:Universidad de ValladolidIngléshttps://www.sciencedirect.com/science/article/pii/S0377221725008501info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc/4.0/oai:uvadoc.uva.es:10324/794522026-06-13T12:44:47Z
dc.title.none.fl_str_mv Characterizing competition ranks within a comprehensive family of position operators
title Characterizing competition ranks within a comprehensive family of position operators
spellingShingle Characterizing competition ranks within a comprehensive family of position operators
Martínez Panero, Miguel
Preference learning
Linear orders
Weak orders
Positions
Ranks
12 Matemáticas
title_short Characterizing competition ranks within a comprehensive family of position operators
title_full Characterizing competition ranks within a comprehensive family of position operators
title_fullStr Characterizing competition ranks within a comprehensive family of position operators
title_full_unstemmed Characterizing competition ranks within a comprehensive family of position operators
title_sort Characterizing competition ranks within a comprehensive family of position operators
dc.creator.none.fl_str_mv Martínez Panero, Miguel
García Lapresta, José Luis
author Martínez Panero, Miguel
author_facet Martínez Panero, Miguel
García Lapresta, José Luis
author_role author
author2 García Lapresta, José Luis
author2_role author
dc.subject.none.fl_str_mv Preference learning
Linear orders
Weak orders
Positions
Ranks
12 Matemáticas
topic Preference learning
Linear orders
Weak orders
Positions
Ranks
12 Matemáticas
description Producción Científica
publishDate 2025
dc.date.none.fl_str_mv 2025
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://doi.org/10.1016/j.ejor.2025.10.030
https://uvadoc.uva.es/handle/10324/79452
url https://doi.org/10.1016/j.ejor.2025.10.030
https://uvadoc.uva.es/handle/10324/79452
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://www.sciencedirect.com/science/article/pii/S0377221725008501
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc/4.0/
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:UVaDOC. Repositorio Documental de la Universidad de Valladolid
instname:Universidad de Valladolid
instname_str Universidad de Valladolid
reponame_str UVaDOC. Repositorio Documental de la Universidad de Valladolid
collection UVaDOC. Repositorio Documental de la Universidad de Valladolid
repository.name.fl_str_mv
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