Iterative inversion of fuzzified neural networks

The inversion of a neural network is a process of computing inputs that produce a given target when fed into the neural network. The inversion algorithm of crisp neural networks is based on the gradient descent search in which a candidate inverse is iteratively refined to decrease the error between its output and the target. In this paper, we derive an inversion algorithm of fuzzified neural networks from that of crisp neural networks. First, we present a framework of learning algorithms of fuzzified neural networks and introduce the idea of adjusting schemes for fuzzy variables. Next, we derive the inversion algorithm of fuzzified neural networks by applying the adjusting scheme for fuzzy variables to total inputs in the input layer. Finally, we make three experiments on the parity-three problem; we examine the effect of the size of training sets on the inversion and investigate how the fuzziness of inputs and targets of training sets affects the inversion.