  The fuzzy $K$-means problem is a popular generalization of the well-known
$K$-means problem to soft clusterings. We present the first coresets for fuzzy
$K$-means with size linear in the dimension, polynomial in the number of
clusters, and poly-logarithmic in the number of points. We show that these
coresets can be employed in the computation of a $(1+\epsilon)$-approximation
for fuzzy $K$-means, improving previously presented results. We further show
that our coresets can be maintained in an insertion-only streaming setting,
where data points arrive one-by-one.
