On fuzzy input data and the worst scenario method

Chleboun, Jan

Applications of Mathematics, Tome 48 (2003) no. 6, pp. 487-496.

Résumé

In practice, input data entering a state problem are almost always uncertain to some extent. Thus it is natural to consider a set $\mathcal U_{\mathrm ad}$ of admissible input data instead of a fixed and unique input. The worst scenario method takes into account all states generated by $\mathcal U_{\mathrm ad}$ 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 $\mathcal U_{\mathrm ad}$ 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 $\mathcal U_{\mathrm ad}$ is available, i.e., $\mathcal U_{\mathrm ad}$ becomes a fuzzy set. In the article, infinite-dimensional $\mathcal U_{\mathrm ad}$ are considered, two ways of introducing fuzziness into $\mathcal U_{\mathrm ad}$ are suggested, and the worst scenario method operating on fuzzy admissible sets is proposed to obtain a fuzzy set of outputs.

Détail

DOI : 10.1023/B:APOM.0000024488.86492.fb

Classification : 03E72, 49N99, 65K99, 90C70, 90C90
Keywords: fuzzy sets; uncertainty; worst scenario method