54 citations · 143 across the 34 of their papers we have counts for
22 papers · 1 filter
An improvement of Random Node Generator for the uniform generation of capacities
Peiqi Sun, Michel Grabisch, Christophe Labreuche
Capacity is an important tool in decision-making under risk and uncertainty and multi-criteria decision-making. When learning a capacity-based model, it is important to be able to…
An approximation algorithm for random generation of capacities
Michel Grabisch, Christophe Labreuche, Peiqi Sun
Capacities on a finite set are sets functions vanishing on the empty set and being monotonic w.r.t. inclusion. Since the set of capacities is an order polytope, the problem of rand…
On the decomposition of Generalized Additive Independence models
Michel Grabisch, Christophe Labreuche
The GAI (Generalized Additive Independence) model proposed by Fishburn is a generalization of the additive utility model, which need not satisfy mutual preferential independence. I…
Exact bounds of the M{ö}bius inverse of monotone set functions
Michel Grabisch, Pedro Miranda
We give the exact upper and lower bounds of the M{ö}bius inverse of monotone and normalized set functions (a.k.a. normalized capacities) on a finite set of n elements. We find that…
On the poset of computation rules for nonassociative calculus
Miguel Couceiro, Michel Grabisch
The symmetric maximum, denoted by v, is an extension of the usual max operation so that 0 is the neutral element, and -x is the symmetric (or inverse) of x, i.e., x v(-x)=0. Howeve…
A Discrete Choquet Integral for Ordered Systems
Ulrich Faigle, Michel Grabisch
A model for a Choquet integral for arbitrary finite set systems is presented. The model includes in particular the classical model on the system of all subsets of a finite set. The…