Model assessment using inverse fuzzy arithmetic

Abstract

A general problem in numerical simulations is the selection of an appropriate model for a given real system. In this paper, the authors propose a new method to validate, select and optimize mathematical models. The presented method uses models with fuzzy-valued parameters, so-called comprehensive models, that are identified by the application of inverse fuzzy arithmetic. The identification is carried out in such a way that the uncertainty band of the output, which is governed by the uncertain input parameters, conservatively covers a reference output. Based on the so identified fuzzy-valued model parameters, a criterion for the selection and optimization is defined that minimizes the overall uncertainty inherent to the model. This criterion does not only consider the accuracy in reproducing the output, but also takes into account the size of the model uncertainty which is necessary to cover the reference output. © Springer-Verlag Berlin Heidelberg 2010.