Applications of Mathematics

Abstract

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