广义Mamdani模糊系统依K-积分模的泛逼近及其实现过程

首先，通过引入拟减法算子给出K-积分模定义，并针对广义Mamdani模糊系统实施等距剖分其输入空间. 其次，应用分片线性函数（Piecewise linear function，PLF）的性质构造性地证明了广义Mamdani模糊系统在K-积分模意义下具有泛逼近性，从而将该模糊系统对连续函数空间的逼近能力扩展到一类可积函数类空间上. 最后，通过模拟实例给出该广义Mamdani模糊系统对给定可积函数的泛逼近及实现过程.

Universal Approximation and Its Realization of Generalized Mamdani Fuzzy System Based on K-integral Norms

Firstly, the definition of a K-integral norm is given by introducing the quasi-subtraction operator, and the input space of a generalized Mamdani fuzzy system is divided by equidistant partition. Secondly, applying some properties of a piecewise linear function (PLF), universal approximation of a generalized Mamdani fuzzy system is proved structurally in the sense of a K-integral norms. Furthermore, the capability of the fuzzy systems to approximate the space of continuous functions is extended into that to a kind of space of integrable functions class. Finally, the universal approximation and its realization of generalized Mamdani fuzzy system to a given integrable function are showed by means of a simulation example.