On robustness for set-valued optimization problems

In the recent past, finding robust solutions for optimization problems contaminated with uncertainties has been topical and has been investigated in the literature for scalar and multi-objective/vector-valued optimization problems. In this paper, we introduce various types of robustness concept for set-valued optimization, such as min–max set robustness, optimistic set robustness, highly set robustness, flimsily set robustness, multi-scenario set robustness. We study some existence results for corresponding concepts of solution and establish some relationship among them.