Fuzzy rule generation via multi-scale clustering

In designing fuzzy logic controllers, various clustering algorithms have been applied to the input space for the purpose of generating fuzzy rules. These algorithms normally assume that the number of clusters or rules is given or known. This paper presents the use of a clustering algorithm, called multi-scale clustering, for generating fuzzy rules without requiring a prescribed number of clusters or rules. This algorithm partitions a space by examining the number of clusters across fine to coarse scale levels. It then determines an optimal number of clusters by using a measure of structural stability named lifetime. This measure reflects the duration across a range of scale levels for which the number of clusters or configuration of rules remains unaltered. The number of clusters with the longest lifetime or the longest lasting rule configuration is then deployed to create fuzzy rules. The classic problem of an inverted pendulum on a cart is presented to show the steps involved when utilizing this algorithm for fuzzy rule generation. This particular example uses a TSK (Takagi-Sugeno-Kang) controller. The input space consists of four dimensions while the output space has one dimension. The prototypes that the algorithm obtains generate the coefficients needed for the TSK model via fuzzy linear approximation. The success of the clustering outcome is evaluated in terms of the resulting number of rules and the ability to duplicate the response of the original system