On interval weighted three-layer neural networks

When solving application problems, the data sets used to train a neural network may not be one hundred percent precise but are within a certain range. By representing data sets with intervals, one has interval neural networks. By analyzing the mathematical model, the authors categorize general three-layer neural network training problems into two types. One of them can be solved by finding numerical solutions of nonlinear systems of equations. The other can be transformed into nonlinear optimization problems. Reliable interval algorithms such as interval Newton/generalized bisection method and interval branch-and-bound algorithm are applied to obtain optimal weights for interval neural networks. Applicable state-of-art interval software packages are also reviewed.