© 1993

Triangular Norm-Based Measures and Games with Fuzzy Coalitions


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

Table of contents

  1. Front Matter
    Pages i-ix
  2. Dan Butnariu, Erich Peter Klement
    Pages 1-5
  3. Dan Butnariu, Erich Peter Klement
    Pages 7-35
  4. Dan Butnariu, Erich Peter Klement
    Pages 37-68
  5. Dan Butnariu, Erich Peter Klement
    Pages 69-98
  6. Dan Butnariu, Erich Peter Klement
    Pages 99-126
  7. Dan Butnariu, Erich Peter Klement
    Pages 127-163
  8. Dan Butnariu, Erich Peter Klement
    Pages 165-188
  9. Back Matter
    Pages 189-201

About this book


This book aims to present, in a unified approach, a series of mathematical results con­ cerning triangular norm-based measures and a class of cooperative games with Juzzy coalitions. Our approach intends to emphasize that triangular norm-based measures are powerful tools in exploring the coalitional behaviour in 'such games. They not and simplify some technical aspects of the already classical axiomatic the­ only unify ory of Aumann-Shapley values, but also provide new perspectives and insights into these results. Moreover, this machinery allows us to obtain, in the game theoretical context, new and heuristically meaningful information, which has a significant impact on balancedness and equilibria analysis in a cooperative environment. From a formal point of view, triangular norm-based measures are valuations on subsets of a unit cube [0, 1]X which preserve dual binary operations induced by trian­ gular norms on the unit interval [0, 1]. Triangular norms (and their dual conorms) are algebraic operations on [0,1] which were suggested by MENGER [1942] and which proved to be useful in the theory of probabilistic metric spaces (see also [WALD 1943]). The idea of a triangular norm-based measure was implicitly used under various names: vector integrals [DVORETZKY, WALD & WOLFOWITZ 1951], prob­ abilities oj Juzzy events [ZADEH 1968], and measures on ideal sets [AUMANN & SHAPLEY 1974, p. 152].


environment fuzzy sets service sets

Authors and affiliations

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

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