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...

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Hauptverfasser:	Butnariu, D. (VerfasserIn), Klement, Erich Peter (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Dordrecht Springer Netherlands 1993
Ausgabe:	1st ed. 1993
Schriftenreihe:	Theory and Decision Library C, Game Theory, Social Choice, Decision Theory, and Optimization 10
Schlagworte:	Operations Research/Decision Theory Measure and Integration Economic Theory/Quantitative Economics/Mathematical Methods Operations research Decision making Measure theory Economic theory Fuzzy-Menge Koalition Spieltheorie
Online-Zugang:	BTU01 Volltext
Zusammenfassung:	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]
Beschreibung:	1 Online-Ressource (X, 202 p)
ISBN:	9789401736022
DOI:	10.1007/978-94-017-3602-2