Interval-valued data are needed to manage either the uncertainty related to measurements, or the variability inherent to the description of complex objects representing group of individuals. We present a new fuzzy c-means type algorithm based on adaptive Euclidean distances with Entropy Regularization for interval-value data. The improvement in comparison with [1] concerns a new automatic weighting scheme for the interval boundaries [2]. Another improvement concerns the intro- duction of entropy regularization. For that aim a regularization term is adjoined to the maximum internal homogeneity criterion [3], that represents the fuzziness in the form of a weighting factor multiplying the contribution of the regularization function to the clustering criterion. The proposed method optimizes an objective function by alternating three steps aiming to compute the fuzzy cluster representatives, the fuzzy partition, as well as relevance weights for the interval-valued variables. Experiments on synthetic and real datasets corroborate the usefulness of the proposed algorithm.