Fuzzy integral representation

In this paper we give representation results for nonlinear functionals in arbitrary spaces, as fuzzy integrals. The main assumption is that of comonotonic maxitivity (i.e. I(f boolean OR g) = If boolean OR Ig for comonotonic f, g). Under the more restrictive condition of stochastic dominance, we prove a more specific representation as a fuzzy integral with respect to a distorted probability measure. We discuss the particular cases of possibility measures and upper fuzzy expectations. Some partial Randon-Nikodym results are proved for both the Choquet and the fuzzy integrals. Finally an example is shown where the fuzzy integral representation is useful.