A new design method called MORDE (multi-objective robust design exploration), which conducts both a multi-objective robust optimization and data mining for analyzing trade-offs, is proposed. For the robust optimization, probabilistic representation of design parameters is incorporated into a multi-objective genetic algorithm. The means and standard deviations of responses of evaluation functions to uncertainties in design variables are evaluated by descriptive Latin hypercube sampling using Kriging surrogate models. To extract trade-off control rules further, a new approach, which combines the association rule with an "aspiration vector, " is proposed. MORDE is then applied to an industrial design problem concerning a centrifugal fan. Taking dimensional uncertainty into account, MORDE then optimized the means and standard deviations of the resulting distributions of fan efficiency and turbulent noise level. The advantages of MORDE over traditional approaches are shown to be the diversity of the solutions and the quantitative controllability of the trade-off balance among multiple objective functions.