Abstract:[Purposes]The objective of this study is to study the properties of the (approximate) robust weak effective solution and the (approximate) robust effective solution of the uncertain multi-objective optimization problem. [Methods]Through the study of the (approximate) optimal solution of the robust scaling problem with relaxation and residual variables, some sufficient conditions and necessary conditions for the (approximate) robust weak effective solution and the (approximate) robust effective solution were established [Findings]The scaling model with relaxation and residual variables proposed by the deterministic multi-objective optimization problem was extended to the robust case, and a new class of robust scaling problems was proposed. [Conclusions]The results obtained are the improvement and promotion of some recent research work..