Robust counterparts and robust efficient solutions in vector optimization under uncertainty

Two robust counterparts and associated concepts of robust efficient solution are established for a vector optimization problem under uncertainty. First, we propose a robust counterpart in the classical sense by following the line for scalar optimization problems under uncertainty. Then, from a relaxed model we derive another robust counterpart, which is a bilevel optimization problem involving a set-valued optimization problem at the upper level and a vector optimization problem at the lower level.