%0 Journal Article
%A Grabisch, Michel
%A Miranda Menéndez, Pedro
%T Exact bounds of the Mobius inverse of monotone set functions
%D 2015
%@ 0166-218X
%U https://hdl.handle.net/20.500.14352/24085
%X 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.
%~