Buckling is typically the governing failure mode of thin-walled shells. In particular, geometric and material imperfections have a major influence on the buckling behavior. Small variations of imperfections have large effects on the load-bearing behavior. However, the design of shells is still characterized by a deterministic way of thinking, in which uncertainties have not yet been sufficiently considered. Even in probabilistic approaches, false assumptions are often generated due to the small amount of experimental data. The focus of this paper is an appropriate uncertainty quantification based on the available data. Therefore, the concept of polymorphic uncertainty modeling is presented on axially loaded shells with different types of imperfections. Finally, an idea for a novel design concept for shells based on a fuzzy-valued safety level is introduced. The paper is intended to initiate a rethinking of the methodology for the numerical design of shells with an appropriate uncertainty quantification.