The application of new mathematical structures to safety analysis

Probabilistic safety analyses (PSAs) often depend on significant subjectivity. The recent successes of fuzzy logic and fuzzy and hybrid mathematics in portraying subjectivity is a reminder that a selection made from the most applicable mathematical tools is more important than forced adaptation of conventional tools. We consider new approaches that enhance conventional and fuzzy PSA by improved handling of subjectivity. The most significant of the mathematical structures we have investigated (from a standpoint of safety analysis applications) are described, and the general types of applications are outlined.