On the axiomatization of some classes of discrete universal integrals

Following the ideas of the axiomatic characterization of the Choquet integral due to [D. Schmeidler, Integral representation without additivity, Proc. Amer. Math. Soc. 97 (1986) 255–261] and of the Sugeno integral given in [J.-L. Marichal, An axiomatic approach of the discrete Sugeno integral as a tool to aggregate interacting criteria in a qualitative framework, IEEE Trans. Fuzzy Syst. 9 (2001) 164–172], we provide a general axiomatization of some classes of discrete universal integrals, including the case of discrete copula-based universal integrals (as usual, the product copula corresponds just to the Choquet integral, and the minimum to the Sugeno integral).