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

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.MareŇ° (Praha)


91A12 Cooperative games
90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming
03E72 Theory of fuzzy sets, etc.