NEURAL NETWORKS WITH INTERVAL WEIGHTS FOR NONLINEAR MAPPINGS OF INTERVAL VECTORS

This paper proposes an approach for approximately realizing nonlinear mappings of interval vectors by interval neural networks. Interval neu ral networks in this paper are characterized by interval weights and i nterval biases. This means that the weights and biases are given by in tervals instead of real numbers. First, an architecture of interval ne ural networks is proposed for dealing with interval input vectors. Int erval neural networks with the proposed architecture map interval inpu t vectors to interval output vectors by interval arithmetic. Some char acteristic features of the nonlinear mappings realized by the interval neural networks are described. Next, a learning algorithm is derived. In the derived learning algorithm, training data are the pairs of int erval input vectors and interval target vectors. Last, using a numeric al example, the proposed approach is illustrated and compared with oth er approaches based on the standard back-propagation neural networks w ith real number weights.