Yoğun Bir Boğazda Çarpışma ve Karaya Oturma Riski İçin Fermatean Bulanık Hata Ağacı ve Bayes Ağı Melez Modeli

Öz

Çarpışma ve karaya oturma, yoğun trafiğe sahip boğazlarda en sık görülen kaza türleridir; bu sularda yoğun kesişen trafik, keskin dönüşler ve kuvvetli akıntılar insan ve teknik kusurlarla birlikte etkili olur. Bu sularda nicel risk değerlendirmesi, kısıtlı arıza verisi ve uzman görüşlerindeki belirsizlik nedeniyle zorlaşmaktadır. Bu çalışma, yoğun bir boğaz geçişinde çarpışma ve karaya oturma riskini değerlendirmek için Fermatean bulanık hata ağacı analizini bir Bayes ağı ile birleştiren melez bir model önermektedir. Uzman dilsel değerlendirmeleri, kübik üyelik ve üye olmama kısıtı sayesinde sezgisel ve Pythagorean bulanık sayılara göre daha geniş bir görüş uzayına izin veren Fermatean bulanık sayılarla temsil edilmektedir. Hata ağacının VEYA ile VE kapıları için yeni Fermatean bulanık kapı işleçleri tanımlanmış ve üç özellik kanıtlanmıştır: işleçlerin Fermatean bulanık tanım kümesinde kapalılığı, skor sıralamasında tekdüzelik ve değerlendirmeler tereddütsüz olduğunda klasik hata ağacı formüllerine indirgenme. Hata ağacı bir Bayes ağına haritalanarak ileri çıkarım ile en üst olay olasılığı, geri çıkarım ile tanısal sonsal olasılıklar ve önem ölçütleri elde edilmektedir. İstanbul Boğazı koşullarını yansıtacak biçimde yapılandırılan örnek olay, üç uzman tarafından değerlendirilen on dört temel olay ile incelenmiştir. Boğaz örneği gösterim amaçlıdır ve temel olay girdileri kaza istatistiklerinden değil uzman görüşlerinden elde edilmiştir. En üst olay olasılığı geçiş başına yaklaşık 0,00097 olarak tahmin edilmiştir. Yetersiz manevra alanı ve omurga altı boşluğu, dönüşlerdeki kuvvetli akıntı ve yakın geçiş durumunun geç fark edilmesi başlıca katkı sağlayan etkenlerdir. Uzman görüş ayrılığı üzerinden yapılan Monte Carlo çözümlemesi yüzde doksanlık güven aralığını 0,00072 ile 0,00151 arasında vermekte ve önem sıralaması 0,95 ortalama sıra ilişkisi ile kararlı kalmaktadır.

Anahtar Kelimeler

• Fermatean bulanık kümeler
• hata ağacı analizi
• Bayes ağı
• denizcilik risk değerlendirmesi
• yoğun boğaz

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

Öz

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.

Anahtar Kelimeler

• Fermatean fuzzy sets
• fault tree analysis
• Bayesian network
• maritime risk assessment
• congested strait

Etik Beyan

No human or animal subjects; ethical approval not required, as stated in the declarations.

Teşekkür

The author sincerely thanks the anonymous reviewers for their careful reading and constructive comments, which have substantially improved the quality and clarity of this manuscript.

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