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In this paper, the experts' opinions are described by linguistic terms which can be expressed in trapezoidal (or triangular) fuzzy numbers. To make the consensus of the experts consistent, we utilize the fuzzy Delphi method to adjust the fuzzy rating of every expert to achieve the consensus condition. To aggregate many experts' opinions, we take the operation of fuzzy numbers to get the mean of fuzzy rating x~/sub if/, and the mean of weight w~/sub aj/. In multi-alternatives and multi-attributes, the fuzzy decision matrix X~=[x~/sub ij/] is constructed by all mean of fuzzy rating, x~/sub if/. Then, We can derive the aggregate fuzzy numbers by multiplying the fuzzy decision matrix with the corresponding fuzzy attribute weight, and the final results become ranking fuzzy numbers problem. We also propose an easy procedure of ranking fuzzy numbers to rank aggregate fuzzy numbers A~/sub j/. In this way, we can obtain the best selection for the evaluating system. For practical application, we proposed an algorithm for evaluating alternative system by a simple fuzzy group decision-making method.