An application of interval-valued neural networks to a regression problem

Abstract

This paper is concerned with exploiting uncertainty in order to develop a robust regression algorithm for a pre-sliding friction process based on a Nonlinear Auto-Regressive with eXogenous inputs neural network. Essentially, it is shown that using an interval-valued neural network allows a trade-off between the model error and the interval width of the network weights or a ‘degree of uncertainty’ parameter. The neural network weights are replaced by interval variables and cannot therefore be derived from a conventional optimization algorithm; in this case, the problem is solved by using differential evolution. The paper also shows how to implement the idea of ‘opportunity’ as used in Ben-Haim's information-gap theory.