Training Fuzzy Number Neural Networks Using Constrained Backpropagation
Few training techniques are available for neural networks with fuzzy number weights, inputs, and outputs. Typically, fuzzy number neural networks are difficult to train because of the many α-cut constraints implied by the fuzzy weights. In this paper, we introduce a weight representation that simplifies the constraint equations. A constrained form of back propagation is then developed for fuzzy number neural networks. Standard backpropagation may be viewed as a constrained optimization of the linearization of the weight function. Our weight representation allows use of the additional α-cut constraints during a weight update.
J. P. Dunyak et al., "Training Fuzzy Number Neural Networks Using Constrained Backpropagation," Fuzzy Systems Proceedings, 1998. IEEE World Congress on Computational Intelligence., vol. 2, pp. 1142-1146, Institute of Electrical and Electronics Engineers (IEEE), Jan 1998.
The definitive version is available at http://dx.doi.org/10.1109/FUZZY.1998.686279
IEEE World Congress on Computational Intelligence (FUZZ-IEEE'98) (1998: May 4-9, Anchorage, AK)
Electrical and Computer Engineering
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© 1998 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.