We characterize those operators that satisfy the properties of monotonicity, permutation invariance, positive homogeneity, and translation invariance. As these operators do not necessarily satisfy comonotonic additivity, their class is larger than that of ordered weighted averaging (OWA) operators. We give a representation theorem for these operators, which shows, nonetheless, that this more general class can be constructed directly from that of OWA operators. In addition, we characterize the special classes consisting of operators that are either subadditive or superadditive. We suggest applications to the evaluation of complex systems.