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 backpropagation 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