In the early stages of project initiation, all aspects of system design may not be clearly defined. Some information might be uncertain (imprecise or vague). However, important design decisions need to be made in these stages in the presence of uncertainty. Fuzzy sets offer a useful method to represent the imprecision in such situations. Fuzzy compromise Decision Support Problems (DSPs) involving fuzzy membership functions are found to be effective in modeling this uncertainty and making decisions in such situations. A hat-shaped, piecewise linear membership function is introduced which is especially useful when the design space is not well understood. The use of a fuzzy compromise Decision Support Problem in the preliminary design synthesis of mechanical systems is illustrated using a case study involving the synthesis of a four-bar linkage.