A Fermatean fuzzy fault tree and Bayesian network hybrid for collision and grounding risk in a congested strait

Collision and grounding remain the dominant accident categories in congested straits, where dense crossing traffic, sharp bends and strong currents act together with human and technical failures. Quantitative risk assessment in such waters is hampered by scarce failure data and by the vagueness of expert judgement. This study proposes a hybrid model that couples Fermatean fuzzy fault tree analysis with a Bayesian network for the assessment of collision and grounding risk during the transit of a congested strait. Expert linguistic judgements are represented by Fermatean fuzzy numbers, whose cubic membership and non-membership constraint admits a wider space of admissible opinions than intuitionistic and Pythagorean fuzzy numbers. New Fermatean fuzzy gate operators are defined for the OR and AND logic of the fault tree. Three properties are proved: closure of the operators within the Fermatean fuzzy domain, monotonicity in the score order and reduction to the classical fault tree formulae when the judgements are non-hesitant. The fault tree is mapped into a Bayesian network so that forward inference yields the top-event probability and backward inference yields diagnostic posteriors and importance measures. A worked case study configured to reflect the Strait of Istanbul is analysed with fourteen basic events assessed by three experts. The strait case is demonstrative and its basic-event inputs are expert-elicited rather than drawn from accident statistics. For this illustrative configuration, the top-event probability is estimated as 9.7 × 10−4 per transit. Inadequate manoeuvring room with under-keel clearance, the strong current at the bends and late detection of close-quarters situations are the leading contributors. A Monte Carlo analysis over expert disagreement gives a ninety per cent credible band of 7.2 × 10−4 to 1.5 × 10−3, and the importance ranking is stable with a mean rank correlation of 0.95.