T-S fuzzy system based on multi-resolution analysis and its function approximation

Inspired by the theory of multi-resolution analysis of wavelet transform, a novel T-S fuzzy system was proposed for approximating nonlinear function. The ante-components of the fuzzy rules are constructed based on the frequency factors, while the consequent parts of the fuzzy rules are consisted of T-S fuzzy subsystems. The fuzzy membership functions of T-S fuzzy subsystems are generated from multi-resolution scale functions. Then, the function approximation of the fuzzy system is analyzed. Subsequently, based on the multi-resolution property of B-spline scale function, a structure identification algorithm of the fuzzy system is proposed. Simulation results show that the fuzzy system is efficient in the approximation of nonlinear function and its fuzzy membership functions have interpretability and multi-resolution characteristic.