Standard Möbius transform evaluation formula for the Choquet integral is associated with the $\mathbf{min}$-aggregation. However, several other aggregation operators replacing $\mathbf{min}$ operator can be applied, which leads to a new construction method for aggregation operators. All binary operators applicable in this approach are characterized by the 1-Lipschitz property. Among ternary aggregation operators all 3-copulas are shown to be fitting and moreover, all fitting weighted means are characterized. This new method allows to construct aggregation operators from simpler ones.