On system identification via fuzzy clustering for fuzzy modeling

Typically, the fuzzy model of the process can be obtained directly from process measurements using an identification method based on fuzzy clustering. However, the number of clusters, which determines the degree of accuracy and complexity of the approximation, must be specified a priori before clustering. In this paper, an efficient method is proposed to determine the number of clusters for fuzzy clustering. A fuzzy equivalence relation is constructed for data points, and a hierarchy of partitions is obtained. To determine the appropriate number of clusters, a cohesion is defined as the relationship between data points in a cluster and coupling is defined as the output spaces. The method proposed is used as a pre-processing step for constructing fuzzy models of electrical discharge machining process. Based on the results of simulation, we find that our hierarchical clustering approach serves as a good method for determining the number of clusters for fuzzy clustering.