ABSTRACT
In this chapter we will give a divisive hierarchical method to detect the cluster structure of a data set X. In this approach the optimal number of clusters in the data set is not known. The method is able to provide the optimal cluster number as well as the corresponding hierarchical cluster structure of X. The cluster structure will be given as a fuzzy hierarchy of data. Let us note that the approach proposed in this chapter may also be useful in the study and design of hierarchically organized fuzzy systems. It may represent a new paradigm of the architecture of complex fuzzy systems. This chapter is based on the papers [5], [7], [8] (see also [12]). Some results are new. The hierarchical agglomerative clustering method of Frigui and Krishnapuram [14] may be regarded as a dual approach of the considered divisive hierarchical one.
