The Bayesian interpretation of Fuzzy C-Means (FCM) opens the door to novel extensions of this technique for soft data clustering. In this paper, we propose a new method based on the minimization of negative log-likelihood of data samples, using basin-hopping and Powell method for minimization. Differently from FCM, we observed a more robust arrangement of prototypes, which could enable the assessment of the suitability of the chosen number of clusters. Moreover, the method enables the data-driven derivation of the fuzzification coefficient, which is directly related to the variance of the component densities. Experiments on synthetic data aim at comparing the proposed method with FCM, by showing benefits and limitations of the two techniques.