Algebraic properties of the Choquet integral

In the paper, we analyze how the properties of the Choquet integral depend on a monotone measure, which are used in integration, namely, based on its characterization in the theory of imprecise probabilities. In particular, using integration, we can generate monotone measures and characterize them by identifying their membership to various families of lower and upper probabilities. In addition, with the help of the Choquet integral, we generate monotone measures on the algebra of fuzzy subsets and analyze their properties. In the paper, we also present a new approach of the Choquet integral axiomatization based on the canonical representation of simple functions.