The rationality of attribute weights determination is an important issue in the weighted fuzzy clustering algorithms. Because of the advantage of describing the fuzziness of decision maker’s inference with interval numbers, attribute weights are represented as intervals, which can be obtained by interval analytic hierarchy process to describe the different contribution of attribute weights for clustering. And a fuzzy c-means algorithm that can obtain attribute weights and clustering results simultaneously is proposed with the interval constraints. The numerical results demonstrate that the proposed algorithm can avoid the iterative calculation from falling into unnecessary local minima under the supervision of the decision maker’s experience and preference, thus the rationality of attribute weights determination is enhanced, and better clustering results can be achieved.