TRIANGULAR NORM~BASED MEASURES and GAMES with FUZZY COALITIONS, Theory And Decision Library C.; Both Author`s Gift Inscription + Signed Letter *

BUTNARIU, D.; KLEMENT, Erich Peter

ISBN 10: 0792323696 / ISBN 13: 9780792323693

Published by Kluwer Academic Publishers, Various Locations * * * * *, 1993

About this Item

Book: Fine/ $297.98 Reduced From. 0792323696 TRIANGULAR NORM~BASED MEASURES and GAMES with FUZZY COALITIONS, Theory And Decision Library C.; Both Author`s Gift Inscription + Signed Letter * BUTNARIU, D.; KLEMENT, Erich Peter Kluwer Academic Publishers 1993 Various Locations * * * * * UnStated 1sT Edition Tall H/c Glossy 0ff~White Spine With Title In Black Letters, Hard Cover Book: Fine/ Slight Shelf, Edge And Corner Wear. 200 Numbered Pages Printed On 0ff~White Paper, Clean And Tight To The Spine, In: Fine/ Condition. Gift Inscription, Inside Front Cover, As Follows, `To Professor L. S. Shapley From Dan Butnariu & Peter Klement`. D/j: None. * = Description Applies To This B00K, Only. = This Author Signed Book Has A Special Significance, Is Hard To Find, Will Be Wrapped In Plastic, Taped Shut, Packaged And Shipped = Carefully, To Avoid Shipping Damage And Will Make It, An Excellent Addition To Your Own Personal Library Collection, Or As A Gift, For The Discriminating Reader / Collector. = No Odors, No Writing, No Names, No Rippling, Not Stuck Together, No Book Plate, Not X~Library, No Remainder Or Other Marks. This Item Will Be Sent Wrapped In Plastic, Taped Shut And In A = Corrugated Mailing B0X = To Prevent Shipping Damage So That It Will Arrive In The Description Described. Description Applies To This B00K, Only. = WORLD WIDE SHIPPING, AVAILABLE. =*=* California State Law Now Requires The Following Notice Be Given: *=*=* Seller Did Not Personally Know This Person Or Persons, And Did Not See And Was Not Present When This Item Was Signed. No Certificate Of Authenticity Is Implied Or Included In This Sale/Purchase Price. If You Would Like A Certificate Of Authenticity, You Can Obtain One At Your Own Convenience And Expense, Which Is Not Included In The Purchase Price Of This Item. =*=*.

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Bibliographic Details

• Title: TRIANGULAR NORM~BASED MEASURES and GAMES with FUZZY COALITIONS, Theory And Decision Library C.; Both Author`s Gift Inscription + Signed Letter *
• Publisher: Kluwer Academic Publishers, Various Locations * * * * *
• Publication Date: 1993
• Language: English
• ISBN 10: 0792323696
• ISBN 13: 9780792323693
• Binding: Hardcover
• Condition: Fine
• Signed: Inscribed by Author(s)

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].

Synopsis

The concept of a value of a coalitional game, in the spirit of R.J. Aumann and L.S. Shapley, is extended to the case of games with fuzzy coalitions, providing heuristically meaningful insights into the game theoretical context, which have some impact on balance and equilibria analysis in a co-operative environment. Using the suggestive and philosophical power of the concept of fuzzy sets introduced by L.A. Zadeh, this text aims to develop the mathematical machinery of triangular norm-based measures, i.e. valuations preserving binary operations induced by triangular norms on [0, 1 ]. These results show the existence of Aumann-Shapley values for large classes of games with fuzzy coalitions satisfying certain differentiability conditions, and allow the extension of the domain of such values to games with crisp coalitions, and the application to real life situations such as rate problems for services in bulk.