Clustering analysis is an important technique in many applications, such as in biology, medicine, psychology, pattern recognition, image processing, marketing, and data engineering. The large number of existing clustering algorithms can be broadly classified into two types: (1) hierarchical and (2) partitional. Depending on the algorithmic approach taken, a hierarchical structure begins with N clusters, one per pattern, and grows a sequence of clusterings until all N patterns are in a single cluster (the agglomerative approach), or begins with one cluster containing all N patterns and successively divides clusters until N clusters are achieved (the divisive approach). Hierarchical clustering is a sequence of nested partitions in the form of a tree diagram or a dendrogram, whereas a partitional clustering is a single partition.
Some fuzzy partitional clustering algorithms and their convergence properties have been given in the literature, but no fuzzy hierarchical clustering algorithm has yet been presented. In this study, fuzzy hierarchical clustering algorithms for the agglomerative approach and the divisive approach, respectively, are proposed. A performance comparison among the two proposed algorithms with different parameter values is included. The two proposed algorithms are compared with two existing algorithms. Additionally, to teduce computational time, the corresponding parallel versions of the two proposed algorithms are developed. Some experimental results show the feasibility of the proposed approaches.