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Triangular Norm-Based Measures and Games with Fuzzy Coalitions

  • Book
  • © 1993

Overview

Authors:
  1. Dan Butnariu

    1. Department of Mathematics and Computer Science, University of Haifa, Israel

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  2. Erich Peter Klement

    1. Institute of Mathematics, Johannes Kepler University, Linz, Austria

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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    • Dan Butnariu, Erich Peter Klement
    Pages 1-5

  3. Triangular Norm-Based Tribes

    • Dan Butnariu, Erich Peter Klement
    Pages 7-35

  4. Triangular Norm-Based Measures

    • Dan Butnariu, Erich Peter Klement
    Pages 37-68

  5. T ∞ -Measures

    • Dan Butnariu, Erich Peter Klement
    Pages 69-98

  6. Games with Fuzzy Coalitions

    • Dan Butnariu, Erich Peter Klement
    Pages 99-126

  7. Extensions of the Diagonal Value

    • Dan Butnariu, Erich Peter Klement
    Pages 127-163

  8. Related Topics and Applications

    • Dan Butnariu, Erich Peter Klement
    Pages 165-188

  9. Back Matter

    Pages 189-201
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Keywords

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].

Authors and Affiliations

  • Department of Mathematics and Computer Science, University of Haifa, Israel

    Dan Butnariu

  • Institute of Mathematics, Johannes Kepler University, Linz, Austria

    Erich Peter Klement

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