This paper is a survey of fuzzy set theory applied in cluster analysis. These fuzzy clustering algorithms have been widely studied and applied in a variety of substantive areas. They also become the major techniques in cluster analysis. In this paper, we give a survey of fuzzy clustering in three categories. The first category is the fuzzy clustering based on fuzzy relation. The second one is the fuzzy clustering based on objective function. Finally, we give an overview of a nonparametric classifier. That is the fuzzy generalized k-nearest neighbor rule. Keywords-cluster analysis, FUZZY clustering, FUZZY c-partitions, FUZZY relation, FUZZY c-means, Fuzzy generalized k-nearest neighbor rule, Cluster validity.