On cores and stable sets for fuzzy games

Tijs, S.H.; Brânzei, R.; Ishihara, S.; Muto, Shigeo

doi:10.1016/s0165-0114(03)00329-4

Cited by 68 publications

(19 citation statements)

References 6 publications

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“…This theory has been developing for decades, but has never been in the mainstream of the fuzzy systems theory (Billot 1998;Butnariu 1978Butnariu , 1987Nurmi 1978;Tijs et al 2004). The fuzzy primitives of the theory: strategies,information, outcomes, payoffs can all be viewed as fuzzy sets.…”

Section: From Fuzzy Choices To Mechanism Designmentioning

confidence: 99%

Fuzzy social choice: a selective retrospect

Nurmi

2007

Soft Comput

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One of the founders of social choice theory, Marquis de Condorcet, assigned truth degrees to propositions expressing preferences over options. Although his work is often discussed in terms of probability theory, it is arguable that his truth degree lends itself to a more natural interpretation as a fuzzy preference. We shall review some of Condorcet's results in the light of this interpretation. The first twentieth century applications of fuzzy concepts to social choice appeared rather shortly after the introduction by L. A. Zadeh of the concept of fuzzy binary relation in early 1970s. The early applications dealt with experimental anomalies and their accountability with the aid of fuzzy preference relations and fuzzy goal states. Considerable literature now exists on various solution concepts in fuzzy voting games and many important theorems of traditional social choice theory have found their counterpart in fuzzy social choice. The natural next step would seem to be the design of fuzzy mechanisms and institutions.

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Section: From Fuzzy Choices To Mechanism Designmentioning

confidence: 99%

Fuzzy social choice: a selective retrospect

Nurmi

2007

Soft Comput

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“…It can be seen as a multichoice game with a continuum of level of participations. Fuzzy games have been studied by Butnariu and Klement [7], and more recently by Branzei and Tijs [6,50].…”

Section: Examples Of Generalized Gamesmentioning

confidence: 99%

Capacities and Games on Lattices: A Survey of Results

Grabisch

2006

Int. J. Unc. Fuzz. Knowl. Based Syst.

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We provide a survey of recent developments about capacities (or fuzzy measures) and ccoperative games in characteristic form, when they are defined on more general structures than the usual power set of the universal set, namely lattices. In a first part, we give various possible interpretations and applications of these general concepts, and then we elaborate about the possible definitions of usual tools in these theories, such as the Choquet integral, the Möbius transform, and the Shapley value.

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“…The Shapley function for fuzzy games is studied by Butnariu (1980), Tsurumi et al (2001), Butnariu and Kroupa (2008), Li and Zhang (2009), Meng and Zhang (2010). The fuzzy core of fuzzy games is focused on by Branzei et al (2003), Tijs et al (2004), Butnariu and Kroupa (2009), Yu and Zhang (2009).…”

Section: Introductionmentioning

confidence: 99%

The fuzzy core and Shapley function for dynamic fuzzy games on matroids

Meng

Zhang

2011

Fuzzy Optim Decis Making

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In this paper, the generalized forms of the fuzzy core and the Shapley function for dynamic fuzzy games on matroids are given. An equivalent form of the fuzzy core is researched. In order to better understand the fuzzy core and the Shapley function for dynamic fuzzy games on matroids, we pay more attention to study three kinds of dynamic fuzzy games on matroids, which are named as fuzzy games with multilinear extension form, with proportional value and with Choquet integral form, respectively. Meantime, the relationship between the fuzzy core and the Shapley function for dynamic fuzzy games on matroids is researched, which coincides with the crisp case.

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On cores and stable sets for fuzzy games

Cited by 68 publications

References 6 publications

Fuzzy social choice: a selective retrospect

Fuzzy social choice: a selective retrospect

Capacities and Games on Lattices: A Survey of Results

The fuzzy core and Shapley function for dynamic fuzzy games on matroids

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