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**Triangular norm-based measures and games with fuzzy coalitions.**
*(English)*
Zbl 0804.90145

Theory and Decision Library. Series C: Game Theory, Mathematical Programming and Operations Research. 10. Dordrecht: Kluwer Academic Publishers. ix, 200 p. (1993).

The book presents in a compact and consistent form a relatively wide scale of topics. The briefly described concepts of triangular norm and conorm are used to introduce the fundamental notion of \(t\)-norm-based measure and to describe its properties. Such measures are used to define and study games with fuzzy coalitions and their solutions where special attention is paid to the Aumann-Shapley value and its diagonal modification. The fuzzy coalitions are defined as fuzzy subsets of a general non-empty set of players where the values of the membership functions represent the share of individual participation of players in particular coalitions. The last chapter of the book deals with a few applications of the general theory (games with crisp coalitions, economic equilibria, plausibility measures, etc.). The book is completed by an index and representative bibliography.

Reviewer: M.Mareš (Praha)