A fuzzy clustering problem consists in assigning a set of patterns to a given number of clusters with respect to some criteria such that each of them may belong to more than one cluster with different degrees of membership. In order to solve it, we first propose a new local search heuristic, called Fuzzy J-Means, where the neighbourhood is defined by all possible centroid-to-pattern relocations. The 'integer' solution is then moved to a continuous one by an alternate step, i.e., by finding centroids and membership degrees for all patterns and clusters. To alleviate the difficulty of being stuck in local minima of poor value, this local search is then embedded into the Variable Neighbourhood Search metaheuristic. Results on five standard test problems from the literature are reported and compared with those obtained with the well-known Fuzzy C-Means heuristic. It appears that solutions of substantially better quality are obtained with the proposed methods than with this former one.