Fuzzy Fault Trees: the Fast and the Formal

We provide a rigorous framework for handling uncertainty in quantitative fault tree analysis based on fuzzy theory. We show that any algorithm for fault tree unreliability analysis can be adapted to this framework in a fully general and computationally efficient manner. This result crucially leverages both the alpha-cut representation of fuzzy numbers and the coherence property of fault trees. We evaluate our algorithms on an established benchmark of synthetic fault trees, demonstrating their practical effectiveness.

💡 Research Summary

The paper introduces a rigorous and computationally efficient framework for incorporating uncertainty into quantitative fault‑tree analysis by leveraging fuzzy set theory. Traditional fault‑tree analysis (FTA) assumes precise failure probabilities for basic events (BEs) and computes system unreliability as the probability that the top event occurs. In many safety‑critical domains, however, these probabilities are not known exactly due to conflicting expert opinions, scarce data, or inherent vagueness. The authors propose to model each basic event’s failure probability as a fuzzy number, i.e., a membership function over the interval