A new sequential learning algorithm using pseudo-Gaussian functions for neuro-fuzzy systems

This paper proposes a framework for constructing and training a radial basis function (RBF) neural network, which is an example of fuzzy system. For this purpose, a sequential learning algorithm is presented to adapt the structure of the network, in which it is possible to create a new hidden unit (rule) and also to detect and remove inactive units. The structure of the gaussian functions (membership functions) is modified using a pseudo-Gaussian function (PG) in which two sealing parameters σ are introduced, which eliminates the symmetry restriction and provides the neurons in the hidden layer with greater flexibility with respect to function approximation. Other important characteristics of the proposed neural system is that instead of using a single parameter for the output weights, these are functions of the input variables which leads to a significant reduction in the number of hidden units compared with the classical RBF network Finally, we examine the result of applying the proposed algorithm to time series prediction