Special issue on “uncertainty modeling and analysis with intervals: foundations, tools, applications”

Abstract

Verification and validation assessment of process modeling and simulation is increasing in importance in various areas of application. They include complex mechatronic and biomechanical tasks with especially strict requirements on numerical accuracy and performance. However, engineers lack precise knowledge regarding the process and its input data. This lack of knowledge and the inherent inexactness in measurement make such general verification and validation cycle tasks as design of a formal model and definition of relevant parameters and their ranges difficult to complete. To assess how reliable a system is, verification and validation analysts have to deal with uncertainty. There are two types of uncertainty: aleatory and epistemic. Aleatory uncertainty refers to variability similar to that arising in games of chance. It cannot be reduced by further empirical study. Epistemic (reducible) uncertainty refers to the incertitude resulting from lack of knowledge. An example is the absence of evidence about the probability distribution of a parameter. Here, interval methods provide a possible solution strategy. Another option, mostly discussed in the context of risk analysis, is to use interval-valued probabilities and imprecisely specified probability distributions. The probability of an event can be specified as an interval; probability bounds analysis propagates constraints on a distribution function through mathematical operations. In a more general setting, the theory of imprecise probabilities is a powerful conceptual framework in which uncertainty is represented by closed, convex sets of probability distributions. Bayesian sensitivity analysis or Dempster-Shafer theory are further options. As the guest editors of this special issue, we are pleased to introduce a collection of articles that were presented and discussed at a Dagstuhl Seminar 11371 (http://www. dagstuhl.de/11371) ‘‘Uncertainty modeling and analysis with intervals—Foundations, tools, applications’’, which took place September 11–16, 2011. The major emphasis of the seminar was on modeling and analyzing uncertainties and propagating them through application systems by using interval arithmetic. This special issue collects twelve papers which present various aspects of the investigations based on interval arithmetic. On one hand, there are theoretical and methodological contributions (Q. Fazal and A. Neumaier, W. Lodwick and O. Jenkins, E. Popova and M. Hladik, F. Zapata et al.). On the other hand, there are presentations of software frameworks for verified scientific computing and modelling of complex uncertain systems (O. Heimlich et al., M. Zimmer et al.), as well as some applications (T. Dotschel et al., S. Kiel et al., P. Shao and N. Stewart). There is also a group of papers which compare or combine interval and probabilistic approaches (M. Beer and V. Kreinovich, G. Rebner et al., Y. Wang). V. Kreinovich (&) Department of Computer Science, University of Texas at El Paso, 500 W. University, El Paso, TX 79968, USA e-mail: vladik@utep.edu