Conditions for Choquet Integral Representation (Choquet)

The Choquet integral with respect to a fuzzy measure is a functional on the class $B$ of measurable functions, that is comonotonically additive and monotone(for short $\mathrm{c}.\mathrm{m}. $). Sugeno et al. [15] proved that a $\mathrm{c}.\mathrm{m} $. functional $I $ can be represented by a Choquet integral with respect to a regular fuzzy measure when the domain of $I $ is the class $K^{+} $ o