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The early phase of design intrinsically contains multiple sources of uncertainty in describing design, and nevertheless the decision-making process at this phase exerts a critical effect upon drawing a successful design. This paper proposes a set-based design approach for multi-objective design problem under uncertainty. The proposed design approach consists of four design processes including set representation, set propagation, set modification, and set narrowing. This approach enables the flexible and robust design while incorporating designer's preference structure. In contrast to existing optimization techniques, this approach generates a ranged set of design solutions that satisfy changing sets of performance requirements.