Multi-objective optimization problems with interval parameters are ubiquitous and important,yet not many effective methods are available for solving them. To solve these problems, we propose a set-based evolutionary algorithm incorporated with decision-maker (DM)’s preferences to obtain a Pareto solution set which satisfies DM’s preferences. In this algorithm, the original optimization problem is first transformed into a tri-objective deterministic optimization problem with three performance indicators: hyper-volume, uncertainty and DM satisfaction. To solve the transformed problem, we employ a set-based Pareto dominance relation to compare different individuals. Individuals with the same rank are distinguished by using a specially designed extension measure incorporating DM’s preferences. Additionally, a set-based mutation and recombination scheme is suggested to generate an offspring with high performance. Four benchmark multiobjective optimization problems and a car cab design problem have been used to evaluate the proposed method; results are compared with those from other three methods. Conclusions indicate that the proposed method can obtain a Pareto solution set with a desirable compromise between the convergence, extension, uncertainty and the DM’s satisfaction.