Effective shape functions for the Generalized Finite Element Method should reflect the available information on the solution. This information is fuzzy because the solution is, of course, unknown, and, typically, the only available information is the solution's inclusion in various function spaces. It is desirable to select shape functions that perform robustly over a family of relevant situations. Quantitative concepts of robustness are introduced and discussed. We show in particular that, in one dimension, polynomial are robust when the only available information consist in inclusions in the usual Sobolev spaces. If some additional information is available, if, e.g., the approximated function is constrained by certain boundary conditions, then polynomials could perform---in the sense of robustness---very badly, and some other family of shape functions should be used. This talk is bases on joint work with I. Babuska and U. Banerjee.