直觉模糊神经网络的函数逼近能力

Function approximation capabilities of intuitionistic fuzzy reasoning neural networks

运用直觉模糊集理论,建立了自适应神经-直觉模糊推理系统(ANIFIS)的控制模型,并证明了该模型具有全局逼近性质.首先将Zadeh模糊推理神经网络变为直觉模糊推理网络,建立一个多输入单输出的T-S型ANIFIS模型;然后设计了系统变量的属性函数和推理规则,确定了各层的输入输出计算关系,以及系统输出结果的合成计算表达式;最后通过证明所建模型的输出结果计算式满足Stone-Weirstrass定理的3个假设条件,完成了该模型的全局逼近性证明.

A controlling model of an adaptive neuro-intuitionistic fuzzy inference system （ANIFIS） is constructed by utilizing intuitionistic fuzzy sets theory with the function approximation property of the model proved. Zadeh fuzzy inference neural nets are developed into intuitionistic fuzzy inference nets, and a model of ANIFIS in Takagi-Sugeno type is established. The attribute functions and the inference rules of the system variables are devised with computational relations between the layers of input and output and a synthesized computational expression of system outputs ascertained. A successful proof of global approximation property of the model is accomplished by testifying that the computational expression of output results of the founded model satisfies the three hypothetic conditions of Stone-Weirstrass theorem.