Abstract
In this paper we discuss integral inequalities for collection integrals that are a special subclass of decomposition integrals introduced as a general framework for many non-linear integrals, including the Choquet integral, the Shilkret integral, the PAN integral, and the concave integral. We give a full characterization of collection integrals that are comonotone additive and for which Chebyshev's, Jensen's, Cauchy's, and Hölder's integral inequalities hold. Interestingly, all these classes of collection integrals coincide and thus we introduce a special subclass of collection integrals, called PCC integrals. The paper is complemented with some examples and remarks for collection and decomposition integrals.
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