Abstract
This chapter opens the fundamental part of the book, focusing on mathematical properties. It presents the main classes of set functions that will be considered throughout the book, namely games (set functions vanishing on the empty set) and capacities (monotone games). In the main part of this chapter (Sects. 2.1– 2.18), we consider set functions defined on a nonempty finite set X, where the domain of set functions is the power set 2X. In Sect. 2.19 we briefly address the case of arbitrary spaces and domains.
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© 2016 Springer International Publishing Switzerland
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Grabisch, M. (2016). Set Functions, Capacities and Games. In: Set Functions, Games and Capacities in Decision Making. Theory and Decision Library C, vol 46. Springer, Cham. https://doi.org/10.1007/978-3-319-30690-2_2
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DOI: https://doi.org/10.1007/978-3-319-30690-2_2
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-30688-9
Online ISBN: 978-3-319-30690-2
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