Two approaches to fuzzification of payments in NTU coalitional game

There exist several possibilities of fuzzification of a coalitional game. It is quite usual to fuzzify, e.\,g., the concept of coalition, as it was done in [1]. Another possibility is to fuzzify the expected pay-offs, see [3,4]. The latter possibility is dealt even here. We suppose that the coalitio...

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Detalhes bibliográficos
Autor: Mareš, Milan
Formato: artículo
Fecha de publicación:2002
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2099/3623
Acesso em linha:https://hdl.handle.net/2099/3623
Access Level:acceso abierto
Palavra-chave:Fuzzification
NTU games
Coaliational games
Jocs, Teoria de
Classificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory
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spelling Two approaches to fuzzification of payments in NTU coalitional gameMareš, MilanFuzzificationNTU gamesCoaliational gamesJocs, Teoria deClassificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theoryThere exist several possibilities of fuzzification of a coalitional game. It is quite usual to fuzzify, e.\,g., the concept of coalition, as it was done in [1]. Another possibility is to fuzzify the expected pay-offs, see [3,4]. The latter possibility is dealt even here. We suppose that the coalitional and individual pay-offs are expected only vaguely and this uncertainty on the "input" of the game rules is reflected also by an uncertainty of the derived "output" concept like superadditivity, core, convexity, and others. This method of fuzzification is quite clear in the case of games with transferable utility, see [6,3]. The not transferable utility (NTU) games are mathematically rather more complex structures. The pay-offs of coalitions are not isolated numbers but closed subsets of n-dimensional real space. Then there potentially exist two possible approaches to their fuzzification. Either, it is possible to substitute these sets by fuzzy sets (see, e.g.[3,4]). This approach is, may be, more sophisticated but it leads to some serious difficulties regarding the domination of vectors from fuzzy sets, the concept of superoptimum, and others. Or, it is possible to fuzzify the whole class of (essentially deterministic) NTU games and to represent the vagueness of particular properties or components of NTU game by the vagueness of the choice of the realized game (see [5]). This approach is, perhaps, less sensitive regarding some subtile variations in the the fuzziness of some properties but it enables to transfer the study of fuzzy NTU coalitional games into the analysis of classes of deterministic games. These deterministic games are already well known, which fact significantly simplifies the demanded analytical procedures. This brief contribution aims to introduce formal specifications of both approaches and to offer at least elementary comparison of their properties.Universitat Politècnica de Catalunya. Secció de Matemàtiques i Informàtica20022002-01-0120072007-10-02journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2099/3623reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2099/36232026-05-27T15:37:01Z
dc.title.none.fl_str_mv Two approaches to fuzzification of payments in NTU coalitional game
title Two approaches to fuzzification of payments in NTU coalitional game
spellingShingle Two approaches to fuzzification of payments in NTU coalitional game
Mareš, Milan
Fuzzification
NTU games
Coaliational games
Jocs, Teoria de
Classificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory
title_short Two approaches to fuzzification of payments in NTU coalitional game
title_full Two approaches to fuzzification of payments in NTU coalitional game
title_fullStr Two approaches to fuzzification of payments in NTU coalitional game
title_full_unstemmed Two approaches to fuzzification of payments in NTU coalitional game
title_sort Two approaches to fuzzification of payments in NTU coalitional game
dc.creator.none.fl_str_mv Mareš, Milan
author Mareš, Milan
author_facet Mareš, Milan
author_role author
dc.subject.none.fl_str_mv Fuzzification
NTU games
Coaliational games
Jocs, Teoria de
Classificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory
topic Fuzzification
NTU games
Coaliational games
Jocs, Teoria de
Classificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory
description There exist several possibilities of fuzzification of a coalitional game. It is quite usual to fuzzify, e.\,g., the concept of coalition, as it was done in [1]. Another possibility is to fuzzify the expected pay-offs, see [3,4]. The latter possibility is dealt even here. We suppose that the coalitional and individual pay-offs are expected only vaguely and this uncertainty on the "input" of the game rules is reflected also by an uncertainty of the derived "output" concept like superadditivity, core, convexity, and others. This method of fuzzification is quite clear in the case of games with transferable utility, see [6,3]. The not transferable utility (NTU) games are mathematically rather more complex structures. The pay-offs of coalitions are not isolated numbers but closed subsets of n-dimensional real space. Then there potentially exist two possible approaches to their fuzzification. Either, it is possible to substitute these sets by fuzzy sets (see, e.g.[3,4]). This approach is, may be, more sophisticated but it leads to some serious difficulties regarding the domination of vectors from fuzzy sets, the concept of superoptimum, and others. Or, it is possible to fuzzify the whole class of (essentially deterministic) NTU games and to represent the vagueness of particular properties or components of NTU game by the vagueness of the choice of the realized game (see [5]). This approach is, perhaps, less sensitive regarding some subtile variations in the the fuzziness of some properties but it enables to transfer the study of fuzzy NTU coalitional games into the analysis of classes of deterministic games. These deterministic games are already well known, which fact significantly simplifies the demanded analytical procedures. This brief contribution aims to introduce formal specifications of both approaches and to offer at least elementary comparison of their properties.
publishDate 2002
dc.date.none.fl_str_mv 2002
2002-01-01
2007
2007-10-02
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2099/3623
url https://hdl.handle.net/2099/3623
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
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http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
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http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
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dc.publisher.none.fl_str_mv Universitat Politècnica de Catalunya. Secció de Matemàtiques i Informàtica
publisher.none.fl_str_mv Universitat Politècnica de Catalunya. Secció de Matemàtiques i Informàtica
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
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