Discussion of approximation error bounds to the class of fuzzy system

The standard fuzzy systems are established with partition of normal quadratic polynomial membership functions and normal trigonometric membership functions. Based on the systems established and the standard fuzzy systems with partition of normal triangle functions, approximation error bounds problems are discussed by interpolation theory. Universal approximation error bounds of these fuzzy systems from SISO to MISO are given and their relations are founded. The error remainder term and auxiliary function are employed for the first time in proving process. Moreover, advantage and shortcoming of the three fuzzy systems are compared and correlative conclusions are obtained. Finally, computing examples are given and the validity of the conclusions is confirmed.