关于两类具有不同基函数的标准模糊系统逼近精度问题的研究

Study on Approaching Precision to Standard Fuzzy Systems with Two Different Basic Functions

在标准模糊系统的基础上提出了以正规二次多项式和正规三角函数为基函数的两类标准模糊系统.通过采用数值分析中的余项与辅助函数方法,对这两类模糊系统进行了误差精度的分析,给出了从SISO到MISO的误差界公式.同时,对这两类模糊系统误差界进行了比较,指出了两类模糊系统的优劣.最后,通过算例验证了理论结果的正确性.

This paper establishes the standard fuzzy systems with partition of normal quadratic polynomial membership functions and normal trigonometric membership functions. Based on above standard fuzzy systems, 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 paper emploies error remainder term and auxiliary function in proving process for the first time. Moreover, advantage and shortcoming of the two fuzzy systems are compared and correlative conclusions are obtained. At last, computing examples are given and the validity of above conclusions is confirmed.