Artificial wavelet neuro-fuzzy model based on parallel wavelet network and neural network

From the well-known advantages and valuable features of wavelets when used in neural network, two type of networks (i.e., SWNN and MWNN) have been proposed. These networks are single hidden layer network. Each neuron in the hidden layer is comprised of wavelet and sigmoidal activation functions. First model is derived from adding the outputs of wavelet and sigmoidal activation functions, while in the second model outputs of wavelet and sigmoidal activation function are multiplied together. Using these proposed networks in consequent part of the neuro-fuzzy model, which result summation wavelet neuro-fuzzy and multiplication wavelet neuro-fuzzy models, are also proposed. Different types of wavelet function are tested with proposed networks and fuzzy models on four different types of examples. Convergence of the learning process is also guaranteed by performing stability analysis using Lyapunov function.