Sequential learning artificial fuzzy neural networks (SLAFNN) with single hidden layer

Abstract

In this paper, a sequential orthogonal approach to the building and training of a single hidden layer fuzzy neural network is presented. Sequential learning artificial neural network model proposed by Zhang and Morris (Neural Networks 11 (1) (1998) 65) is modified to tackle fuzzy inputs and crisp outputs and a sequential learning artificial fuzzy neural network model is developed and used in this paper. This model can tackle the common problem encountered by conventional fuzzy back propagation neural network in the determination of the network structure in the number of hidden layers and the number of hidden neurons in each layer. Non-linear mapping between fuzzy input vectors and crisp output is performed. Left and right (LR) type representation is used to reduce the network complexity. A simple defuzzification process is proposed. The procedure starts with a single hidden neuron and sequentially increases in the number of hidden neurons until the model error is sufficiently small. The classical Gram–Schmidt orthogonalization method is used at each step to form a set of orthogonal bases for the space spanned by output vectors of the hidden neurons. In this approach it is possible to determine the necessary number of hidden neurons required. The fuzzy neural network architecture has been trained and tested to civil engineering problems such as determination of allowable stress limits for a beam subjected to lateral loads, earthquake damage and the evaluation of wind pressure predictions.