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Grabisch, Michel and Miranda Menéndez, Pedro (2015) Exact bounds of the Mobius inverse of monotone set functions. Discrete applied mathematics, 186 . pp. 7-12. ISSN 0166-218X
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Official URL: http://www.sciencedirect.com/science/article/pii/S0166218X15000189
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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Möbius inverse; Monotone set function; Interaction |
| Subjects: | Sciences > Mathematics > Mathematical statistics |
| ID Code: | 31327 |
| Deposited On: | 07 Jul 2015 09:05 |
| Last Modified: | 07 Jul 2015 10:59 |
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