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This paper presents a new method for handling the fuzzy clustering problems of which the characteristic values and weights of the indices are generalized fuzzy numbers. The proposed mechanism is based on the fuzzy-number similarity measure. First, the proposed method determines the linguistic evaluating values and the linguistic weights of each evaluating criterion with respect to the alternatives. Thereafter, it measures the degree of similarity between two arbitrary weighted evaluating values on the same criterion. Finally, it constructs a hierarchical cluster tree and generates differing clusters. A numerical example was demonstrated using the new method.