Games with Fuzzy Coalitions

Part of the Theory and Decision Library book series (TDLC, volume 10)


In this chapter the set X is interpreted as a set of players who participate in interactive activities by forming fuzzy coalitions,i.e., coalitions which they may belong to in various degrees. Such a coalition will be represented by a fuzzy subset of X. If A is a fuzzy subset of X representing a fuzzy coalition, then we interprete the membership degree of a player xX to A as the share of the individual worth of the player x which is invested as his participation in the fuzzy coalition A. In a specific social environment the class of fuzzy coalitions which can be effectively constituted by the players is determined by exogeneous rules. We always assume that this class is a T -tribe.ℐ which is given a priori, and the term fuzzy coalition is used to determine an element of.ℐ. A game on.ℐ or, simply, a game is a function v: ℐ → ℝ with v(Ø) = 0. The class of all games on ℐ is denoted GAMES or, simply, GAMES,when there is no possibility of confusion. GAMES ,is an algebra with the operations naturally induced from ℝ.


Additive Function Linear Subspace Bounded Variation Fuzzy Subset Market Game 
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Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of HaifaIsrael
  2. 2.Institute of MathematicsJohannes Kepler UniversityLinzAustria

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