Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 456919, 25 pages
Research Article

A Smoothing Interval Neural Network

School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Received 23 May 2012; Accepted 18 October 2012

Academic Editor: Daniele Fournier-Prunaret

Copyright © 2012 Dakun Yang and Wei Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In many applications, it is natural to use interval data to describe various kinds of uncertainties. This paper is concerned with an interval neural network with a hidden layer. For the original interval neural network, it might cause oscillation in the learning procedure as indicated in our numerical experiments. In this paper, a smoothing interval neural network is proposed to prevent the weights oscillation during the learning procedure. Here, by smoothing we mean that, in a neighborhood of the origin, we replace the absolute values of the weights by a smooth function of the weights in the hidden layer and output layer. The convergence of a gradient algorithm for training the smoothing interval neural network is proved. Supporting numerical experiments are provided.