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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https://hal.archives-ouvertes.fr/hal-01136668
Contributor : Michel Grabisch <>
Submitted on : Friday, March 27, 2015 - 5:41:47 PM
Last modification on : Wednesday, March 28, 2018 - 2:38:54 PM

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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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