Function approximation via particular input space partition and region-based exponential membership functions. (Q1430892)

A new fuzzy modeling approach is proposed to approximate unknown functions from numerical data. Instead of using the clustering-based fuzzy model procedure, the input space is partitioned into several characteristic regions, making sure that input-output pairs of the same region are strictly increasing or decreasing for all input variables. According to the coordinates of input-output pairs in the Cartesian product space, the proposed algorithm partitions the input space into several characteristic regions, whose boundaries are determined by the local-minimum, local-maximum and turning points of the training data. The region-based exponential functions are chosen as membership functions of antecedents, with consequents of rules as singletons, thus constructing the fuzzy model. First, a brief review of the fuzzy inference for the problem of function approximation is given. Next, a detailed procedure of the algorithm and a simple example for illustration are provided. Five examples are given to show the performance of the presented method.