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Fuzzy integral representation. (English) Zbl 0906.28009

Summary: 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., \(I(f\vee g)= If\vee Ig\) 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 Radon-Nikodým results are proved for both the Choquet and the fuzzy integrals. Finally, an example is shown where the fuzzy integral representation is useful.

MSC:

28E10 Fuzzy measure theory
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