The knowledge about available resources during high-level synthesis is usually imprecise. Previous methods seem to have ignored this fact, possibly to avoid an increase in the, already high, computational complexity. In this paper an approach based on so called "possibilistic" programming, a kind of fuzzy mathematical programming, is presented. Using this method we can improve existing mathematical programming methods for the architectural synthesis while keeping their good properties. Not only architectures which optimize the most possible value of the cost function can be generated, but more importantly, also the tradeoff between this goal and reducing the probability of obtaining worse solution and enhancing probability of obtaining a better solution is controlled. At the same time, an increase in the computational complexity of the algorithms is avoided. To show the validity of the approach an application to simultaneous scheduling, selection and allocation of functional units is described. The approach has been implemented in a system called FOAS. Experimental results confirm the advantages of the proposed methodology.