An extension of the BP-algorithm to interval input vectors-learning from numerical data and expert´s knowledge

The authors extend the backpropagation algorithm to the case of interval input vectors. First, for two-group classification problems of interval vectors, they propose a neural network architecture which can deal with interval input vectors. Since the proposed architecture maps an interval input vector into an interval, the output from the neural network is an interval. The authors define a cost function using the target output and the interval output from the neural network. The learning algorithm derived from the cost function can be viewed as an extension of the backpropagation algorithm to the case of interval input vectors. The algorithm can deal with both real vectors and interval vectors as input vectors of the neural network. Therefore, in learning of the neural network, one can use the expert´s knowledge represented by means of intervals