A new membership function approach to uncertain functions.

A fuzzy set approach to uncertain functions is in the focus of this paper. The uncertainty in functions entering a model, a differential equation, for instance, is represented by α -dependent sets of crisp functions, that is, α -cuts determined by an integral membership functional that is defined by means of a continuous auxiliary function whose design depends on the information the analyst has about the uncertainty. A scalar quantity of interest evaluating the model output is assumed and its membership function is inferred from the Zadeh extension principle by solving α -dependent worst- and best-case scenario problems. Two types of auxiliary functions are considered and their algorithmic advantages and disadvantages are discussed. [ABSTRACT FROM AUTHOR]