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INICIO | 10 de diciembre de 2023

Two approaches to fuzzification of payments in NTU coalitional game.

Título inglés Two approaches to fuzzification of payments in NTU coalitional game.
Título español Dos enfoques para la borrosificación de los pagos en juegos cooperativos NTU.
Autor/es Mares, Milan
Organización Inst. Inform. Theor. Autom. Acad. Sci. Czech Repub. (UTIA AV CR), Praga, Repúb. Checa
Revista 1134-5632
Publicación 2002, 9 (2-3): 129-136, 6 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés 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.
Clasificación UNESCO 110208 ; 120706
Palabras clave español Lógica difusa ; Juegos cooperativos
Código MathReviews MR1983788
Código Z-Math Zbl 1037.91016
Icono pdf Acceso al artículo completo
Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)