Today's electronic devices must meet many requirements, such as those related to performance, limits to the radiated electromagnetic field, size, etc. For such a design, the requirement is to have a solution that simultaneously meets multiple objectives that sometimes include conflicting requirements. In addition, it is also necessary to consider uncertain parameters. This paper proposes a new combination of statistical analysis using the Polynomial Chaos (PC) method for dealing with the random and multi-objective satisfactory design using the Preference Set-based Design (PSD) method. The application in this paper is an Electromagnetic Interference (EMI) filter for a practical case, which includes plural element parameters and uncertain parameters, which are resistors at the source and load, and the performances of the attenuation characteristics. The PC method generates simulation data with high enough accuracy and good computational efficiency, and these data are used as initial data for the meta-modeling of the PSD method. The design parameters of the EMI filter, which satisfy required performances, are obtained in a range by the PSD method. The authors demonstrate the validity of the proposed method. The results show that applying a multi-objective design method using PSD with a statistical method using PC to handle the uncertain problem can be applied to electromagnetic designs to reduce the time and cost of product development.