  We introduce a functor of functionals which preserve maximum of comonotone
functions and addition of constants. This functor is a subfunctor of the
functor of order-preserving functionals and contains the idempotent measure
functor as subfunctor. The main aim of this paper is to show that this functor
is isomorphic to the capacity functor. We establish such isomorphism using the
fuzzy max-plus integral. In fact, we can consider this result as an idempotent
analogue of Riesz Theorem about a correspondence between the set of
$\sigma$-additive regular Borel measures and the set of linear positively
defined functionals.
