Exact bounds of the Möbius inverse of monotone set functions
Journal article: 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.
Author(s)
Michel Grabisch, Pedro Miranda
Journal
- Discrete Applied Mathematics
Date of publication
- 2015
Keywords
- Möbius inverse
- Monotone set function
- Interaction
Pages
- 7-12
URL of the HAL notice
Version
- 1
Volume
- 186