  We aim at representing the recently introduced conditional aggregation-based
Choquet integral as a standard Choquet integral on a hyperset. The
representation is one of transformations considered by R.R. Yager and R. Mesiar
in 2015. Thus we study the properties of the conditional aggregation-based
Choquet integral using well-known facts about the standard Choquet integral. In
particular, we obtain several formulas for its computation. We also provide the
representation of the conditional aggregation-based Choquet integral in terms
of the M\"obius transform.
