A method is proposed to deal with multiple-alternative decision problems under uncertainty. It is assumed that all the alternatives in the choice set can be characterized by a number of aspects, and that information is available to assign weights to these aspects and to construct a rating scheme for the various aspects of each alternative. The method basically consists of computing weighted final ratings for each alternative and comparing the weighted final ratings. The uncertainty that is assumed to be inherent in the assessments of the ratings and weights is accounted for by considering each of these variables as fuzzy quantities, characterized by appropriate membership functions. Accordingly, the final evaluation of the alternatives consists of a degree of membership in the fuzzy set of alternatives ranking first. A practical method is given to compute membership functions of fuzzy sets induced by mappings, and applied to the problem at hand. A number of examples are worked out. The method is compared to another one proposed by Kahne who approaches the problem probabilistically.