Numerical analysis of the learning of fuzzified neural networks from fuzzyif-then rules

The main aim of this paper is to clearly show how fuzzified neural networks are trained by back-propagation-type learning algorithms for approximately realizing fuzzy if-then rules. Our fuzzified neural network is a three-lay er feedforward neural network where connection weights are fuzzy numbers. A set of fuzzy if-then rules is used as training data for the learning of ou r fuzzified neural network. That is, inputs and targets are linguistic valu es such as "small" and "large". In this paper, we first demonstrate that th e fuzziness in training data propagates backward in our fuzzified neural ne twork. Next we examine the ability of our fuzzified neural network to appro ximately realize fuzzy if-then rules. In computer simulations, we compare f our types of connection weights (i.e., real numbers, symmetric triangular f uzzy numbers, asymmetric triangular fuzzy numbers, and asymmetric trapezoid al fuzzy numbers) in terms of the fitting ability to training data and the computation time. We also examine a partially fuzzified neural network. In our partially fuzzified neural network, connection weights and biases to ou tput units are fuzzy numbers while those to hidden units are real numbers. Simulation results show that such a partially fuzzified neural network is a good hybrid architecture of fully fuzzified neural networks and neural net works with non-fuzzy connection weights. (C) 2001 Elsevier Science B.V. All rights reserved.