Artículos (Matemática Aplicada II)

URI permanente para esta colecciónhttps://hdl.handle.net/11441/10899

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Fuzzy restrictions and an application to cooperative games with restricted cooperation
(Taylor and Francis, 2017-05) Gallardo Morilla, José Manuel; Jiménez Jiménez, María Nieves; Jiménez Losada, Andrés; Universidad de Sevilla. Departamento de Matemática Aplicada II; Spanish Ministry of Economy and Competitiveness ECO2010-17766; Andalusian Government grant FQM237; Universidad de Sevilla. FQM237: Juegos con Estructuras Combinatorias y de Orden
The concept of restriction, which is an extension of that of interior operator, was introduced to model limited cooperation in cooperative game theory. In this paper, a fuzzy version of restrictions is presented. We show that these new operators, called fuzzy restrictions, can be characterized by the transitivity of the fuzzy dependence relations that they induce. As an application, we introduce cooperative games with fuzzy restriction, which are used to model cooperative situations in which each player in a coalition has a level of cooperation within the coalition. A value for these games is defined and characterized.
Games with fuzzy authorization structure: a Shapley value
(Elsevier, 2015-08) Gallardo Morilla, José Manuel; Jiménez Jiménez, María Nieves; Jiménez Losada, Andrés; Lebrón Rueda, Esperanza Angustias; Universidad de Sevilla. Departamento de Matemática Aplicada II; Spanish Ministry of Economy and Competitiveness ECO2010-17766; Andalusian Government grant FQM237; Universidad de Sevilla. FQM237: Juegos con Estructuras Combinatorias y de Orden
A cooperative game consists of a set of players and a characteristic function which determines the maximal gain or minimal cost that every subset of players can achieve when they decide to cooperate, regardless of the actions that the other players take. It is often assumed that the players are free to participate in any coalition, but in some situations there are dependency relationships among the players that restrict their capacity to cooperate within some coalitions. Those relationships must be taken into account if we want to distribute the profits fairly. In this respect, several models have been proposed in literature. In all of them dependency relationships are considered to be complete, in the sense that either a player is allowed to fully cooperate within a coalition or they cannot cooperate at all. Nevertheless, in some situations it is possible to consider another option: that a player has a degree of freedom to cooperate within a coalition. A model for those situations is presented.
Games with fuzzy permission structure: A conjunctive approach
(Elsevier, 2014-09) Gallardo Morilla, José Manuel; Jiménez Jiménez, María Nieves; Jiménez Losada, Andrés; Lebrón Rueda, Esperanza Angustias; Universidad de Sevilla. Departamento de Matemática Aplicada II; Spanish Ministry of Economy and Competitiveness ECO2010-17766; Andalusian Government grant FQM237; Universidad de Sevilla. FQM237: Juegos con Estructuras Combinatorias y de Orden
A cooperative game consists of a set of players and a characteristic function which determines the maximal gain or minimal cost that every subset of players can achieve when they decide to cooperate, regardless of the actions that the other players take. A permission structure over the set of players describes a hierarchical organization where there are players who need permission from certain other players before they are allowed to cooperate with others. Various assumptions can be made about how a permission structure affects the cooperation possibilities. In the conjunctive approach it is assumed that each player needs permission from all his superiors. This paper deals with fuzzy permission structures in the conjunctive approach. In this model, players could depend partially on other players, that is, they may have certain degree of autonomy. First, we define a value for games with fuzzy permission structure that only takes into account the direct relations among players and provide a characterization for this value. Finally, we study a value for games with fuzzy permission structure which takes account of the indirect relations among players.

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Examinando Artículos (Matemática Aplicada II) por Agencia financiadora "Andalusian Government grant FQM237"