The design approach described in this paper permits designers to deal with imprecisely specified parameters when using the finite element method. In this practical context, the approach allows an efficient, systematic exploration of the entire design space, and it allows designers to show a relative preference for points in that space. The heart of the approach is fuzzy set theory which we adapted for use with finite element analysis by implementing Zadeh's extension principle for implicit functions, and for functions having minima and maxima within the search space. Since the analysis can involve a large amount of computation, we investigated ways to reduce computing time -- one such employs fuzzy sensitivities and is described herein. To illustrate the approach for car body structure NVH design we include several simple but realistic examples.