  In decision-making under uncertainty, several criteria have been studied to
aggregate the performance of a solution over multiple possible scenarios. This
paper introduces a novel variant of ordered weighted averaging (OWA) for
optimization problems. It generalizes the classic OWA approach, which includes
robust min-max optimization as a special case, as well as min-max regret
optimization. We derive new complexity results for this setting, including
insights into the inapproximability and approximability of this problem. In
particular, we provide stronger positive approximation results that
asymptotically improve the previously best-known bounds for the classic OWA
approach. In computational experiments, we evaluate the quality of the proposed
methods and compare the proposed setting with classic OWA and min-max regret
approaches.
