The information in system design procedures is often incomplete and requires intuition of the designer. In conjunction with fuzzy inferences, the possibility theory enables quantification of the uncertainties estimated by human intuition. In light of the notion of possibility, a design procedure is implemented to identify feasible solutions that ensure a certain confidence level. The design alternatives are found via a multi-objective evolutionary algorithm. The method is applied to the sizing problem of a gyrodyne configuration which employs a tip-jet-driven rotor on top of a fixed-wing aircraft.