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

In: Numerical Mathematics and Advanced Applications

Author

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  • J. Chleboun

    (Academy of Sciences, Institute of Mathematics
    Czech Technical University, Faculty of Engineering)

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.

Suggested Citation

  • J. Chleboun, 2008. "The Worst Scenario Method: A Red Thread Running Through Various Approaches to Problems with Uncertain Input Data," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 3-14, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_1
    DOI: 10.1007/978-3-540-69777-0_1
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