Abstract: The paper establishes the standard fuzzy systems with partition of normal quadratic polynomial membership functions and normal trigonometric membership functions. The comparison problems of fuzzy system with normal triangle membership functions and the two fuzzy systems are put forward. Based on above standard fuzzy systems, approximation error bounds are discussed by interpolation theory. Universal approximation error bounds of these fuzzy systems from SISO to MISO are given and their relations are established. The paper employs error remainder term and auxiliary function in the proving process for the first time. Moreover, advantages and shortcomings of these fuzzy systems are compared and correlative conclusions are obtained. At last, computing examples are given and the validity of the conclusions is confirmed.