  In decision analysis and especially in multiple criteria decision analysis,
several non additive integrals have been introduced in the last years. Among
them, we remember the Choquet integral, the Shilkret integral and the Sugeno
integral. In the context of multiple criteria decision analysis, these
integrals are used to aggregate the evaluations of possible choice
alternatives, with respect to several criteria, into a single overall
evaluation. These integrals request the starting evaluations to be expressed in
terms of exact-evaluations. In this paper we present the robust Choquet,
Shilkret and Sugeno integrals, computed with respect to an interval capacity.
These are quite natural generalizations of the Choquet, Shilkret and Sugeno
integrals, useful to aggregate interval-evaluations of choice alternatives into
a single overall evaluation. We show that, when the interval-evaluations
collapse into exact-evaluations, our definitions of robust integrals collapse
into the previous definitions. We also provide an axiomatic characterization of
the robust Choquet integral.
