Function approximation via particular input space partition and region-based exponential membership functions

This paper presents an algorithm to build a compact fuzzy model for approximating unknown nonlinear functions. 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, to construct the fuzzy model. Finally, five examples demonstrate that the proposed fuzzy model indeed improves performance in the approximating of nonlinear functions.