Exact bounds of the Möbius inverse of monotone set functions

Article dans une revue: 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.

Auteur(s)

Michel Grabisch, Pedro Miranda

Revue
  • Discrete Applied Mathematics
Date de publication
  • 2015
Mots-clés
  • Möbius inverse
  • Monotone set function
  • Interaction
Pages
  • 7-12
Version
  • 1
Volume
  • 186