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  "body": "\n## Summary\n\nThe Choquet integral integrates a non-negative function against a [[fuzzy measure|CRFQEGJDA9]], which need not be additive.\nIt adds up the sizes of the level sets $\\set{f \\ge t}$ over all levels $t$, as in the [[layer cake representation|H78RXJC1K1]].\nFor an ordinary measure it agrees with the Lebesgue integral, but in general it is not additive in the function.\nIt is used in decision theory, where it models attitudes towards uncertainty, and in the theory of capacities.\n\n## Explanations\n\n### L1 human\n\nTo integrate a non-negative function, cut its graph into thin horizontal slices.\nAt height $t$, the slice covers the set where the function is at least $t$.\nThe Choquet integral measures each such set with the given set function and adds up the slices over all heights.\nWith a non-additive set function, two functions can each have integral zero while their sum has a positive integral.\n",
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