The properties of the (approximate) robust weak effective solutions and the (approximate) robust effective solutions of the uncertain multi-objective optimization problem are studied. Through the study of the (approximate) optimal solution of the robust scalarization 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 are established. The scalarization model with relaxation and residual variables proposed by the deterministic multi-objective optimization problem is extended to the robust case, and a new class of robust scalarization problems is proposed. The results obtained are the improvement and promotion of some recent research work.