Min-max and min-min robustness are two extreme approaches discussed for single-objective robust optimization problems. Recently, multi-objective robust optimization problems are studied and robust Pareto efficiency definitions have been proposed. In particular, the set-based min-max robust efficiency defined for multi-objective robust optimization problems is analogous to the min-max robust optimality definition for single-objective robust optimization problems. In this study, we define the set-based min-min robust efficiency in addition to the existing definition of the min-max robust efficiency for multi-objective robust optimization problems. We discuss a method to determine the set of set-based min-max robust efficient solutions and propose an evolutionary algorithm to approximate this set. Furthermore, a modification of the algorithm is discussed to approximate the set of set-based min-min robust Pareto efficient solutions. The outcomes based on the two robust efficiency, i.e., set-based min-max and set-based min-min, are compared using numerical examples. Our results show that set-based min-min robust efficiency can be used by optimistic decision makers and can be combined with set-based min-max robust efficiency to model the preferences of the decision makers, who are not ultimately pessimistic
