基于三角形模糊化的非线性T-S模糊系统对p-可积函数的逼近性

Approximation of nonlinear T-S fuzzy system to p-integrable functions based on the triangular fuzzifier

通过给定p-可积函数,引入了分片线性函数(PLF)的解析表达式.基于三角形模糊化、乘积推理机和中心平均解模糊化构造了一类新的非线性T-S模糊系统,在p-积分模下证得非线性T-S模糊系统对此分片线性函数具有逼近性,进而得到该系统对p-可积函数亦具逼近性能.

The analytical expression of piecewise linear function is firstly introduced by agiven p-integrable function.We constitute a class of new nonlinear T-S fuzzy system based on the triangular fuzzifier,product inference engine and center average defuzzifier.It is proved that the nonlinear T-S fuzzy system can approximate the piecewise linear function in the sense of p-integral norm,and also can approximate a p-integrable function with respect to p-integral norm.