以正规多项式为基函数的标准模糊系统逼近误差公式证明

Formula proof of standard fuzzy systems with normal quartic polynomial membership functions as basic functions

为提高模糊系统的逼近精度及扩大基函数的选择范围,定义了论域的正规二次多项式模糊划分.在标准模糊系统的基础上,提出以正规二次多项式为基函数的一类模糊系统;通过采用数值分析中的余项与辅助函数方法,对该类模糊系统进行了逼近误差精度的理论分析,给出了从SISO到MISO的一阶和准二阶误差逼近精度公式;指出该系统逼近精度公式使用的约束条件及应注意的问题.

The paper developed a normal quartic polynomial partition of fuzzy domain and established the standard fuzzy system with partition of normal quadratic polynomial membership functions to improve approximation precision of fuzzy system and extend the fuzzy basic functions. Based on above standard fuzzy system, approximation error formula were discussed by interpolation theory. A first order and approximative second universal approximation error bounds from SISO to MISO were given and their relations were founded. The paper employed error remainder term and auxiliary function in proving process while the used conditions and relative problems of these formula were pointed out in fuzzy systems theory and actual application.