Uçar E., Karageyik B. B.
FUZZY SETS AND SYSTEMS, cilt.109891, sa.109891, ss.109891, 2026 (SCI-Expanded, Scopus)
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Yayın Türü:
Makale / Tam Makale
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Cilt numarası:
109891
Sayı:
109891
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Basım Tarihi:
2026
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Doi Numarası:
10.1016/j.fss.2026.109891
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Dergi Adı:
FUZZY SETS AND SYSTEMS
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Derginin Tarandığı İndeksler:
Scopus, Science Citation Index Expanded (SCI-EXPANDED), Compendex, INSPEC, MathSciNet, zbMATH
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Sayfa Sayıları:
ss.109891
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Ankara Üniversitesi Adresli:
Evet
Özet
This study develops a fuzzy-based approximation framework for aggregate claims modeling in the compound Poisson model by embedding parameter uncertainty into classical approximation schemes. Symmetric triangular fuzzy numbers are constructed from confidence intervals and propagated through the model using first-order approximations within the framework of Zadeh’s extension principle to obtain fuzzy counterparts of normal and translated-gamma approximations. The resulting fuzzy outputs provide both membership-based uncertainty descriptions and centroid-defuzzified values suitable for actuarial calculations.
A numerical case study, benchmarked against Panjer’s recursion, shows that the proposed fuzzy approximations achieve close agreement with the reference results while explicitly capturing parameter uncertainty. The translated gamma-based approach generally provides the closest fit, while the defuzzified fuzzy normal approximation improves upon the classical normal approximation. Overall, the framework provides a transparent and computationally tractable way to assess aggregate losses under both randomness and parameter uncertainty.