Choquet integral

Summary

The Choquet integral integrates a non-negative function against a fuzzy measure, which need not be additive. It adds up the sizes of the level sets $\set{f \ge t}$ over all levels $t$, as in the layer cake representation. For an ordinary measure it agrees with the Lebesgue integral, but in general it is not additive in the function. It is used in decision theory, where it models attitudes towards uncertainty, and in the theory of capacities.