On system identification via fuzzy clustering for fuzzy modeling

The area of fuzzy modeling encompasses several kinds of models that use various concepts from fuzzy sets theory to construct abstract models of systems. Typically, the fuzzy model of the process can be obtained directly from process measurements using an identification method based on fuzzy clustering. Domains of the problem, i.e., input, output and state variables, are partitioned into overlapping regions via 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 appropriate number of clusters, cohesion is defined to be the relatedness between data points in a cluster and coupling is defined to be the relatedness between data points in different clusters. An objective function is developed so as to maximize the cohesion between data points in the same cluster and minimize the coupling between data points in different clusters. The number of clusters when objective function is optimized is used in fuzzy clustering for input and output spaces. The method proposed is used as a preprocessing step for constructing fuzzy models of EDM (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.