Mixed Radix Systems of Fully Connected Neuro-Fuzzy Inference Systems with Special Properties

In this paper, based on the transformation from the fuzzy inference system into a fully connected neural network, F-CONFIS, the mixed radix systems in Fully Connected Neural Fuzzy Inference Systems are derived. The functional equivalence between a fuzzy system and a neural network has been proved, however, they are non-constructive. F-CONFIS provides constructive steps to build the equivalence between a neuro-fuzzy system and a NN. F-CONFIS differs from traditional neural networks by its special properties and can be considered as the variation of a kind of multilayer neural network. It is important to find the mixed radix systems and the properties of this new type of fuzzy neural networks properties so that the training algorithm can be properly carried out for the F-CONFIS. The simulation results indicate that the proposed approach achieves excellent performance.