In the design of electrical contacts, it is required to pursue a solution which satisfies simultaneously multi-objective (electrical, mechanical, and thermal) performances including conflicting requirements. Preference Set-Based Design (PSD) has been proposed as practical procedure of the fuzzy set-based design method. This brief paper newly attempts to propose a concurrent design method by PSD to electrical contact, specifically a design of a shape of cantilever in relay contacts. In order to reduce the calculation (and/or experimental) cost, this paper newly attempt to apply Design of Experiments (DoE) for meta-modeling to PSD. The number of the calculation for the meta-modeling can be reduced to $\frac{1}{729}$ by using DoE. The design parameters (width and length) of a cantilever for drive an electrical contact, which satisfy required performance (target deflection), are obtained in ranges successfully by PSD. The validity of the design parameters is demonstrated by numerical modeling.