In decision making under uncertainty, several criteria have been studied to
aggregate the performance of a solution over multiple possible scenarios,
including the ordered weighted averaging (OWA) criterion and min-max regret.
This paper introduces a novel generalization of min-max regret, leveraging the
modeling power of OWA to enable a more nuanced expression of preferences in
handling regret values. This new OWA regret approach is studied both
theoretically and numerically. We derive several properties, including
polynomially solvable and hard cases, and introduce an approximation algorithm.
Through computational experiments using artificial and real-world data, we
demonstrate the advantages of our OWAR method over the conventional min-max
regret approach, alongside the effectiveness of the proposed clustering
heuristics