Exact bounds of the Möbius inverse of monotone set functions

Abstract : We give the exact upper and lower bounds of the Möbius inverse of monotone and normalized set functions (a.k.a. normalized capacities) on a finite set of n elements. We find that the absolute value of the bounds tend to 4 n/2 √ πn/2 when n is large. We establish also the exact bounds of the interaction transform and Banzhaf interaction transform, as well as the exact bounds of the Möbius inverse for the subfamilies of k-additive normalized capacities and p-symmetric normalized capacities.
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Article dans une revue
Discrete Applied Mathematics, Elsevier, 2015, 186, pp.7-12
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Contributeur : Michel Grabisch <>
Soumis le : vendredi 27 mars 2015 - 17:41:47
Dernière modification le : mercredi 28 mars 2018 - 14:38:54

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  • HAL Id : hal-01136668, version 1
  • ARXIV : 1503.08550

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Michel Grabisch, Pedro Miranda. Exact bounds of the Möbius inverse of monotone set functions. Discrete Applied Mathematics, Elsevier, 2015, 186, pp.7-12. 〈hal-01136668〉

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