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On fuzzy input data and the worst scenario method. (English) Zbl 1099.90081
Summary: In practice, input data entering a state problem are almost always uncertain to some extent. Thus it is natural to consider a set $$\mathcal U_{\text{ad}}$$ of admissible input data instead of a fixed and unique input. The worst scenario method takes into account all states generated by $$\mathcal U_{\text{ad}}$$ 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 $$\mathcal U_{\text{ad}}$$ as equally important though this can be unrealistic and can lead to too pessimistic conclusions. Often, however, additional information expressed through membership function of $$\mathcal U_{\text{ad}}$$ is available, i.e., $$\mathcal U_{\text{ad}}$$ becomes a fuzzy set. In the article, infinite-dimensional $$\mathcal U_{\text{ad}}$$ are considered, two ways of introducing fuzziness into $$\mathcal U_{\text{ad}}$$ are suggested, and the worst scenario method operating on fuzzy admissible sets is proposed to obtain a fuzzy set of outputs.

##### MSC:
 90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
##### Keywords:
fuzzy sets; uncertainty; worst scenario method
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##### References:
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