Set Functions, Games and Capacities in Decision Making [Paperback]

The book provides a thorough treatment of set functions, games and capacities as well as integrals with respect to capacities and games, in a mathematical rigorous presentation and in view of application to decision making. After a short chapter introducing some required basic knowledge (linear programming, polyhedra, ordered sets) and notation, the first part of the book consists of three long chapters developing the mathematical aspects. This part is not related to a particular application field and, by its neutral mathematical style, is useful to the widest audience. It gathers many results and notions which are scattered in the literature of various domains (game theory, decision, combinatorial optimization and operations research). The second part consists of three chapters, applying the previous notions in decision making and modelling: decision under uncertainty, decision with multiple criteria, possibility theory and Dempster-Shafer theory.

Introduction.- Set functions, capacities and games.- The core and the selectope of games.- Integrals.- Decision under risk and uncertainty.- Decisions with multiple criteria.- Dempster-Shafer and possibility theory.

Michel Grabisch has fully succeeded in transforming his deep knowledge of the field into a very rich and quite readable text.

Professor Denis Bouyssou, Universit? Paris Dauphine

This monograph provides a much-needed perspective on a rich collection of structural properties of set functions which have been investigated for more than 60 years, but which have never been collected in a single volume. By establishing these results in a clear and rigorous mathematical framework, the author makes them accessible to a broad audience. His book should rapidly become a classic reference in the field.

Professor Yves Crama, University of Li?ge and HEC Li?ge

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