Min-Max Type Multi-Objective Programming Problem

Let f i , j = 1, …, N, be the criterion functions that depend on the decision maker’s variable x∈ R n and opponent’s (or disturbance) variables yi ∈ R mj, j =1, …, N. In the absence of information about the opponent’s strategies a conservative decision maker would assume that he will experience the worst possible outcome at the hands of his opponents. In such a case, the objective functions to be minimized by the decision maker are defined as follows: