We propose a new method of design called MORDE (multi-objective robust design exploration) that combines a multi-objective robust optimization approach and data-mining techniques for analyzing trade-offs. The probabilistic representation of design parameters, which is compatible with the Taguchi method, is incorporated into the optimization system we previously developed that uses a multi-objective genetic algorithm. The means and standard deviations of responses of evaluation functions against uncertainties in design variables are evaluated by descriptive Latin hypercube sampling using Kriging surrogate models. Design space is visualized by Self-organizing map (SOM). To extract design rules further, a new approach that adopts the association rule with an "aspiration vector" is proposed. MORDE is then applied to an industrial design problem with a centrifugal fan for a washer-dryer. Taking dimensional uncertainty into account, we optimize the means and standard deviations of the resulting distributions of the fan efficiency and turbulent noise level. Steady Reynolds-averaged Navier Stokes simulations are carried out to collect the necessary dataset for Kriging models. We demonstrate the advantages of the proposed method of multi-objective robust optimization over traditional non-robust ones in that the solutions are diverse. We clarify that the association rule can extract both sufficient and necessary conditions as design rules to achieve trade-off balances. The association rule is also more beneficial than SOM in finding quantitative relations, particularly those that are concerned with more than three design parameters.