Pii: S0893-6080(00)00085-x

A modi®cation of the fuzzy backpropagation (FBP) algorithm called QuickFBP algorithm is proposed, where the computation of the net function is signi®cantly quicker. It is proved that the FBP algorithm is of exponential time complexity, while the QuickFBP algorithm is of polynomial time complexity. Convergence conditions of the QuickFBP, resp. the FBP algorithm are de®ned and proved for: (1) single output neural networks in case of training patterns with different targets; and (2) multiple output neural networks in case of training patterns with equivalued target vector. They support the automation of the weights training process (quasi-unsupervised learning) establishing the target value(s) depending on the network's input values. In these cases the simulation results con®rm the convergence of both algorithms. An example with a large-sized neural network illustrates the signi®cantly greater training speed of the QuickFBP rather than the FBP algorithm. The adaptation of an interactive web system to users on the basis of the QuickFBP algorithm is presented. Since the QuickFBP algorithm ensures quasi-unsupervised learning, this implies its broad applicability in areas of adaptive and adaptable interactive systems, data mining, etc. applications. q 2001 Elsevier Science Ltd. All rights reserved.