A method to find solutions to multi-objective design problems that involve poor information available was proposed. The method quantified the designers intuition in a systematic manner, and utilized it to approximate inaccurate and/or vague numbers. In the context of possibility theory, uncertain values were expressed through possibility distributions, i.e. fuzzy membership functions. Based on the membership functions of the value, levels of confidence of the solutions to multi-objective problems were defined through the notions of possibility and necessity. An evolutionary algorithm was modified to find sets of solutions that allow certain levels of confidence instead of the crisp sets of the solutions. The method was applied to a design problem of the gyrodyne configuration and sets of the solutions of the specified possibility and necessity were found. The results of the design problem and the suggestions for future research were discussed.