Clustering can be classified as Hard Clustering (or Exclusive Clustering) and Soft Clustering (Overlapping Clustering). Hard Clustering allow us to discriminate clearly whether an instance belongs to a cluster or not. However, such a partition is insufficient to represent many real situations. Often, an instance cannot be thought of as belonging to a single cluster only, and also is necessary to evaluate what degree do the instances belong to the clusters. The concept of hard and fuzzy partitions proposed by Jim Bezdek in 1981, allows us to extend the notion of membership of instances to clusters. The lecture will present some fuzzy clustering algorithms based on the extensions of popular partitive clustering algorithms through the fuzzy set theory and the possibility theory.