Triangular Norm-Based Measures and Games with Fuzzy Coalitions; Theory and Decision Library C, 10;

Butnariu, D. and Erich Peter Klement:

ISBN 10: 0792323696 / ISBN 13: 9780792323693

Published by Kluwer Aademic Publishers, 1993

About this Item

200 Seiten; Der Erhaltungszustand des hier angebotenen Werks ist trotz seiner Bibliotheksnutzung sehr sauber. Es befindet sich neben dem Rückenschild lediglich ein Bibliotheksstempel im Buch; ordnungsgemäß entwidmet. In ENGLISCHER Sprache. Sprache: Englisch Gewicht in Gramm: 550.

Seller Inventory # 2040422

Bibliographic Details

• Title: Triangular Norm-Based Measures and Games with Fuzzy Coalitions; Theory and Decision Library C, 10
• Publisher: Kluwer Aademic Publishers
• Publication Date: 1993
• Language: English
• ISBN 10: 0792323696
• ISBN 13: 9780792323693
• Binding: gebundene Ausgabe
• Condition: Gut
• Weight: 550 grams
• Seller catalogs:
  • 200 Mathematik

About this title

Synopsis

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].