Continuous m-dimensional distorted probabilities

Fuzzy measures, also known as non-additive measures, monotonic games, and capacities, have been used in many contexts. For example, in economics, risk analysis, in computer science, computer vision and machine learning and, in general, in mathematics. However, when looking at applications, one of th...

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Detalhes bibliográficos
Autores: Torra i Reventós, Vicenç, Guillén, Montserrat, Santolino, Miguel
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2018
País:España
Recursos:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/120168
Acesso em linha:https://hdl.handle.net/2445/120168
Access Level:acceso abierto
Palavra-chave:Lògica borrosa
Probabilitats
Fuzzy logic
Probabilities
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spelling Continuous m-dimensional distorted probabilitiesTorra i Reventós, VicençGuillén, MontserratSantolino, MiguelLògica borrosaProbabilitatsFuzzy logicProbabilitiesFuzzy measures, also known as non-additive measures, monotonic games, and capacities, have been used in many contexts. For example, in economics, risk analysis, in computer science, computer vision and machine learning and, in general, in mathematics. However, when looking at applications, one of the problems that still needs to be solved is how the measure should be defined in an easy and intuitive way. When the reference set is finite, a few families of measures have been established, e.g. distorted probabilities, k-additive and decomposable measures. But, when the reference set is infinite, the only family is distorted probabilities. In this paper we give a definition for m-dimensional distorted probabilities in the case that the reference set is not finite, and we study some properties of this family. We also give a definition for hierarchically decomposable m-dimensional distorted probabilities that relates to another family of measures defined for the finite case.Elsevier B.V.2018202020182018info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersion6 p.application/pdfapplication/pdfhttps://hdl.handle.net/2445/120168Articles publicats en revistes (Econometria, Estadística i Economia Aplicada)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésVersió postprint del document publicat a: https://doi.org/10.1016/j.inffus.2017.12.004Information Fusion, 2018, vol. 44, p. 97-102https://doi.org/10.1016/j.inffus.2017.12.004cc-by-nc-nd (c) Elsevier B.V., 2018http://creativecommons.org/licenses/by-nc-nd/3.0/esinfo:eu-repo/semantics/openAccessoai:recercat.cat:2445/1201682026-05-29T05:05:01Z
dc.title.none.fl_str_mv Continuous m-dimensional distorted probabilities
title Continuous m-dimensional distorted probabilities
spellingShingle Continuous m-dimensional distorted probabilities
Torra i Reventós, Vicenç
Lògica borrosa
Probabilitats
Fuzzy logic
Probabilities
title_short Continuous m-dimensional distorted probabilities
title_full Continuous m-dimensional distorted probabilities
title_fullStr Continuous m-dimensional distorted probabilities
title_full_unstemmed Continuous m-dimensional distorted probabilities
title_sort Continuous m-dimensional distorted probabilities
dc.creator.none.fl_str_mv Torra i Reventós, Vicenç
Guillén, Montserrat
Santolino, Miguel
author Torra i Reventós, Vicenç
author_facet Torra i Reventós, Vicenç
Guillén, Montserrat
Santolino, Miguel
author_role author
author2 Guillén, Montserrat
Santolino, Miguel
author2_role author
author
dc.subject.none.fl_str_mv Lògica borrosa
Probabilitats
Fuzzy logic
Probabilities
topic Lògica borrosa
Probabilitats
Fuzzy logic
Probabilities
description Fuzzy measures, also known as non-additive measures, monotonic games, and capacities, have been used in many contexts. For example, in economics, risk analysis, in computer science, computer vision and machine learning and, in general, in mathematics. However, when looking at applications, one of the problems that still needs to be solved is how the measure should be defined in an easy and intuitive way. When the reference set is finite, a few families of measures have been established, e.g. distorted probabilities, k-additive and decomposable measures. But, when the reference set is infinite, the only family is distorted probabilities. In this paper we give a definition for m-dimensional distorted probabilities in the case that the reference set is not finite, and we study some properties of this family. We also give a definition for hierarchically decomposable m-dimensional distorted probabilities that relates to another family of measures defined for the finite case.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018
2018
2020
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/120168
url https://hdl.handle.net/2445/120168
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: https://doi.org/10.1016/j.inffus.2017.12.004
Information Fusion, 2018, vol. 44, p. 97-102
https://doi.org/10.1016/j.inffus.2017.12.004
dc.rights.none.fl_str_mv cc-by-nc-nd (c) Elsevier B.V., 2018
http://creativecommons.org/licenses/by-nc-nd/3.0/es
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-nc-nd (c) Elsevier B.V., 2018
http://creativecommons.org/licenses/by-nc-nd/3.0/es
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 6 p.
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier B.V.
publisher.none.fl_str_mv Elsevier B.V.
dc.source.none.fl_str_mv Articles publicats en revistes (Econometria, Estadística i Economia Aplicada)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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