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The recording of symbolic interval data has become a common practice with the recent advances in database technologies. This paper introduces fuzzy clustering algorithms to partitioning symbolic interval data. The proposed methods furnish a fuzzy partition and a prototype (a vector of intervals) for each cluster by optimizing an adequacy criterion that measures the fitting between the clusters and their representatives. To compare symbolic interval data, the methods use a suitable (adaptive and non-adaptive) L2 norm defined on vectors of intervals. Experiments with real and synthetic symbolic interval data sets showed the usefulness of the proposed method.