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uncertain input data; the worst-case approach; fuzzy sets
An introduction to the worst scenario method is given. We start with an example and a general abstract scheme. An analysis of the method both on the continuous and approximate levels is discussed. We show a possible incorporation of the method into the fuzzy set theory. Finally, we present a survey of applications published during the last decade.
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[21] I. Hlaváček: Post-buckling range of plates in axial compression with uncertain initial imperfections. Appl. Math. 47 (2002), 25–44. DOI 10.1023/A:1021702816894 | MR 1876490
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[29] I. Hlaváček, J. Nedoma: Reliable solution of a unilateral contact problem with friction and uncertain input data in thermoelasticity. Math. Comput. Simul. 67 (2005), 559–580. DOI 10.1016/j.matcom.2004.08.001 | MR 2111780
[30] I. Hlaváček: Unilateral contact with Coulomb friction and uncertain input data. Numer. Funct. Anal. Optimization 24 (2003), 509–530. DOI 10.1081/NFA-120023866 | MR 1995999 | Zbl 1049.49007
[31] I. Hlaváček, J. Plešek, and D. Gabriel: Validation and sensitivity study of an elastoplastic problem using the worst scenario method. Comput. Methods Appl. Mech. Eng. 195 (2006), 763–774. DOI 10.1016/j.cma.2005.02.010 | MR 2183622
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[35] L. Nechvátal: Worst scenario method in homogenization. Linear case. Appl. Math. 51 (2006), 263–294. DOI 10.1007/s10492-006-0015-9 | MR 2228666 | Zbl 1164.35317
[36] T. Roubíček: Relaxation in Optimization Theory and Variational Calculus. Walter de Gruyter, Berlin, 1997. MR 1458067
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[38] H.-J. Zimmermann: Fuzzy Set Theory—and Its Applications. Kluwer Academic Publishers, Boston, 2001. MR 1882395
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