Triangular Norm-Based Measures and Games with Fuzzy Coalitions

D. Butnariu, Erich Peter Klement (Autoren)

Buch | Hardcover

202 Seiten

1993 | 1993 ed.
Kluwer Academic Publishers (Verlag)
978-0-7923-2369-3 (ISBN)

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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].

I Triangular Norm—Based Tribes.- II Triangular Norm—Based Measures.- III T?—Measures.- IV Games with Fuzzy Coalitions.- V Extensions of the Diagonal Value.- VI Related Topics and Applications.

Erscheint lt. Verlag	30.9.1993
Reihe/Serie	Theory and Decision Library C ; 10
Zusatzinfo	X, 202 p.
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
	Wirtschaft ► Allgemeines / Lexika
	Wirtschaft ► Betriebswirtschaft / Management
ISBN-10	0-7923-2369-6 / 0792323696
ISBN-13	978-0-7923-2369-3 / 9780792323693
Zustand	Neuware