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 new and heuristically meaningful insights into the game theoretical context, which have some significant impact on balance and equilibria analysis in a cooperative environment. Using the suggestive and philosophical power of the concept of fuzzy sets introduced by L.A. Zadeh we develop the mathematical machinery of triangular norm-based measures, i.e. valuations preserving binary operations induced by triangular norms on [0,1]. Our results not only prove the existence of Aumann--Shapley values for large classes of games with fuzzy coalitions satisfying certain differentiability conditions, but also 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.
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This book aims to present, in a unified approach, a series of mathematical results concerning triangular norm-based measures and a class of cooperative games with fuzzy coalitions. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
standardness assumption, crisp coalitions, fuzzy coalitions, monotone games, generated tribes, measurability structure, telephone billing rates, diagonal formula, crisp subsets, spanning subset, diagonal value, symmetric subspace, ordinal sum, triangular norms, positive integer powers, plausibility measures, lower variation, fuzzy subsets, fuzzy measures, fuzzy sets, competitive equilibria, market games Key Phrases - Capitalized Phrases (CAPs): (learn more)
Monotone Convergence Theorem, Classical Values Revisited New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This book aims to present, in a unified approach, a series of mathematical results concerning triangular norm-based measures and a class of cooperative games with fuzzy coalitions. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
standardness assumption, crisp coalitions, fuzzy coalitions, monotone games, generated tribes, measurability structure, telephone billing rates, diagonal formula, crisp subsets, spanning subset, diagonal value, symmetric subspace, ordinal sum, triangular norms, positive integer powers, plausibility measures, lower variation, fuzzy subsets, fuzzy measures, fuzzy sets, competitive equilibria, market games Key Phrases - Capitalized Phrases (CAPs): (learn more)
Monotone Convergence Theorem, Classical Values Revisited New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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- The Shapley Value: Essays in Honor of Lloyd S. Shapley by Alvin E. Roth in Back Matter
- Probability Theory (De Gruyter Studies in Mathematics) by Heinz Bauer in Back Matter
- Jordan Decompositions of Generalized Vector Measures (Research Notes in Mathematics Series) by Klaus D. Schmidt in Back Matter
- Convex Analysis (Princeton Landmarks in Mathematics and Physics) by Ralph Tyrell Rockafellar in Back Matter
- Axiomatic Bargaining Game Theory (Theory and Decision Library C) by H.J. Peters in Back Matter
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- Logical, Algebraic, Analytic and Probabilistic Aspects of Triangular Norms by Erich Peter Klement on page 11, page 54, and page 148
- Language, Quantum, Music (Synthese Library) by Maria Luisa Dalla Chiara on page 260
- New Trends in Quantum Structures (Mathematics and Its Applications (closed)) by Anatolij Dvurecenskij in Back Matter
- Soft Computing in Human-Related Sciences (International Series on Computational Intelligence) by Horia-Nicolai L Teodorescu on page 66
- Social Ties and Economic Performance (Theory and Decision Library C) by Frans van Dijk in Back Matter
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