The Worst Scenario Method: A Red Thread Running Through Various Approaches to Problems with Uncertain Input Data

J. Chleboun ()
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J. Chleboun: Academy of Sciences, Institute of Mathematics

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 3-14 from Springer

Abstract: Abstract Three ingredients constitute mathematical models dependent on parameters whose value is uncertain: a compact set uad of admissible parameters a, a state problem A(a)u = f(a) with an a-dependent state u ≡ u(a), and a continuous quantity of interest Ψ(a) = Φ(a,u(a)). In the worst scenario method (WSM), the maximum of Ψ over uad is identified. By mastering the WSM and if an adequate characterization of input uncertainty is available, the analyst can easily step forward to a more complex uncertainty analysis, namely that based on the Dempster-Shafer theory or fuzzy set theory. Elements of the above non-stochastic approaches to uncertainty modeling are presented with the emphasis on uncertain functions appearing in problems driven by differential equations.

Date: 2008
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DOI: 10.1007/978-3-540-69777-0_1

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