Universal approximation of TS fuzzy systems constructed dynamically-MISO cases

Study on approximation capabilities of fuzzy systems has been an important and hot issue for many years. Many existing studies on fuzzy systems based on standard affine TS fuzzy models suffer seriously from curse of dimensionality though such models are relatively simple to construct; whereas other investigations based on hierarchical fuzzy models have to face the difficulty of relatively more complexity. Through utilizing the dynamic partition along all dimensions, this paper proposes a novel dynamically constructive method in MISO cases to construct fuzzy systems based on standard affine TS fuzzy models, which have simple structures and also can ease the serious curse of dimensionality greatly. Correspondingly, new sufficient conditions for a affine TS fuzzy system as an universal approximator are obtained. The situation in 2ISO cases is derived first which is then extended to general MISO cases. Theoretical analyses comparing to some typical methods and several numerical examples all confirm that the dynamic method in this paper can reduce the fuzzy rules number dramatically and therefore can ease the serious curse of dimensionality to some extent. Some conclusions and discussions on further work are also given.