Interval Finite Elements as a Basis for Generalized Models of Uncertainty in Engineering Mechanics

Latest scientific and engineering advances have started to recognize the need of defining multiple types of uncertainty. Probabilistic modeling cannot handle situations with incomplete or little information on which to evaluate a probability, or when that information is nonspecific, ambiguous, or conflicting [1]. Many generalized models of uncertainty have been developed to treat such situations. Among them, there are five major frameworks that use interval-based representation of uncertainty, namely: imprecise probabilities, possibility theory, DempsterShafer theory of evidence, Fuzzy set theory, and convex set modeling. Regardless what model is adopted, the proper interval solution will represents the first requirement for any further rigorous formulation.