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Abstract: In practice, input data entering a state problem are almost always uncertain to some extent. Thus it is natural to consider a set \Cal U_{\ad} of admissible input data instead of a fixed and unique input. The worst scenario method takes into account all states generated by \Cal U_{\ad} and maximizes a functional criterion reflecting a particular feature of the state solution, as local stress, displacement, or temperature, for instance. An increase in the criterion value indicates a deterioration in the featured quantity. The method takes all the elements of \Cal U_{\ad} as equally important though this can be unrealistic and can lead to too pessimistic conclusions. Often, however, additional information expressed through a membership function of \Cal U_{\ad} is available, i.e., \Cal U_{\ad} becomes a fuzzy set. In the article, infinite-dimensional \Cal U_{\ad} are considered, two ways of introducing fuzziness into \Cal U_{\ad} are suggested, and the worst scenario method operating on fuzzy admissible sets is proposed to obtain a fuzzy set of outputs. |
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