  We propose a novel method for building fuzzy clusters of large data sets,
using a smoothing numerical approach. The usual sum-of-squares criterion is
relaxed so the search for good fuzzy partitions is made on a continuous space,
rather than a combinatorial space as in classical methods \cite{Hartigan}. The
smoothing allows a conversion from a strongly non-differentiable problem into
differentiable subproblems of optimization without constraints of low
dimension, by using a differentiable function of infinite class. For the
implementation of the algorithm we used the statistical software $R$ and the
results obtained were compared to the traditional fuzzy $C$--means method,
proposed by Bezdek.
