A generalization of \(p\)-boxes to affine arithmetic (Q411436)

Input variables with both interval and probabilistic uncertainties can be modelled by \(p\)-boxes and Dempster-Shafer structures (see, e.g., [\textit{S. Ferson, V. Kreinovich, L. Ginzburg, D. S. Myers} and \textit{K. Sentz}, ``Constructing probability boxes and Dempster-Shafer structures'', SAND report, SAND2002-4015 (2003), \url{http://www.sandia.gov/epistemic/Reports/SAND2002-4015.pdf}). Affine arithmetic is an extension of interval arithmetic (see [\textit{J. L. D. Comba} and \textit{J. Stolfi}, ``Affine arithmetic and its application to computer graphics'', Proc. SIBGRAPI'93 -- VI Simpósio Brasileiro de Computação Gráfica e Processamento de Imagens, Recife, Brasil, 9--18 (1993), \url{http://graphics.stanford.edu/~comba/papers/aa-93-09-sibgrapi-paper.pdf}]). In this paper, the authors combine both approaches and use some information about variable dependencies which leads to an increase in precision of the results and a decrease of computation time.