Publication: Exact bounds of the Mobius inverse of monotone set functions
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Publication Date
2015-05-11
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Elsevier
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Abstract
We give the exact upper and lower bounds of the Mobius 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)/root pi n/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 Mobius inverse for the subfamilies of k-additive normalized capacities and p-symmetric normalized capacities.