Characterizations of multi-objective robustness solutions defined by Minkowski set difference

This paper focuses on characterizing the optimality of a kind of partial set order robust solutions, which are defined by Minkowski set difference, for an uncertain multi-objective optimization problem via oriented distance function and image space analysis. Firstly, the relationships between partial set order robust efficiency and upper (lower) set order robust efficiency are illustrated. Secondly, the optimality conditions to partial set order robust solutions are presented by utilizing image space analysis. Furthermore, characterizations are also established for partial set order robust solutions under the assumption of generalized monotonicity, which is determined by an oriented distance function. Finally, an application, namely a shortest path problem, is discussed to verify the effectiveness for the obtained results.