Improving the performance of fuzzy systems by using local partitioning

A method of input space partitioning is presented. It uses a quad tree structure, B-spline functions as fuzzy basis functions and a multiresolution aspect inspired by the wavelet theory. Only the basis functions for the coarsest level are needed. Thereafter, the other basis functions for the finer levels can be formed iteratively. As the different scales of resolution and the corresponding basic elements are formed, a wavelet transform using those basis functions as scaling functions is applied to a data set. The details (wavelet coefficients) are used to prune the quad tree to find the final partition suitable for the problem. Finally, the method is tested with two example problems. Also some common partitioning techniques are reviewed.