Exact bounds of the Möbius inverse of monotone set functions

Michel Grabisch and Pedro Miranda ()
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Pedro Miranda: UCM - Universidad Complutense de Madrid = Complutense University of Madrid [Madrid]

PSE-Ecole d'économie de Paris (Postprint) from HAL

Abstract: 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.

Keywords: Möbius inverse; monotone set function; interaction (search for similar items in EconPapers)
Date: 2015-03-27
Note: View the original document on HAL open archive server: https://hal.science/hal-01136668v1
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Published in Discrete Applied Mathematics, 2015, 186, pp.7-12

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Related works:
Working Paper: Exact bounds of the Möbius inverse of monotone set functions (2015)
Working Paper: Exact bounds of the Möbius inverse of monotone set functions (2015)
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