An Output-Constrained Clustering Approach for the Identification of Fuzzy Systems and Fuzzy Granular Systems

This paper presents an output-constrained clustering approach for fuzzy system identification and fuzzy granular system identification. The approach is unlike most existing clustering algorithms for structure identification of fuzzy systems, where the focus is on input or combined input-output clustering. The output-constrained clustering algorithm divides the output space into several partitions and each output partition is considered to be a constraint; then, input data are projected into clusters that are based on the input distribution constrained by the output partitions. By introducing the key concept of separability of a set of clusters within each output constraint, the proposed approach automatically finds an appropriate small and efficient number of clusters for each output constraint. To have an appropriate small and efficient number of clusters in each output constraint results in a more compact final system structure and better accuracy. This better performance is illustrated by experiments using benchmark function approximation and dynamic system identification.