Work

Material selection for aircraft wing spars under uncertainty using Fermatean fuzzy Z-number neutrality aggregation operators

Year: 2026

Type: article

Abstract: There is a need for practical frameworks to assess multiple material characteristics, handle fuzzy expert judgments, and quantify the confidence in those judgments when identifying reliable materials for safety-critical aerospace structures. Most existing aggregation techniques in fuzzy environments do not consider reliability information. While these methods may produce mathematically sound rankings, their practical value remains limited. To fill this gap, this study provides a solid theoretical basis for the neutrality-based aggregation in the Fermatean fuzzy Z-number (FFZN). A novel family of aggregation operators (AO) is introduced, together with novel operational laws, into the environment. Specifically, using weighted averaging, ordered weighted averaging, geometric averaging, ordered weighted geometric, hybrid weighted averaging, and hybrid weighted geometric AOs are built on the FFZN neutrality architecture, aimed at capturing not only the inherent vagueness of expert evaluations but also the confidence level of each assessment. A structured multi-criteria decision-making (MCDM) and the criteria-wise aggregation are formulated, followed by the reliability integration. The framework is used for selecting composite materials for aircraft wing spars, which are structures with high requirements in a component that has to meet high loading and performance demands that conflict on many criteria concerning load transfer between the wing and fuselage, such as specific strength, fatigue life, defect rate in manufacturing, and material cost. Four candidate materials that could potentially come together to form a composite material are assessed. By applying the proposed MCDM procedure, the obtained rankings are compared with the well-known methods such as WASPAS, CoCoSo, TOPSIS, and VIKOR. The FFZN neutrality AOs provide more stable and discriminative rankings than existing methods for high-stakes engineering problems, where evaluative vagueness and assessment reliability must be rigorously accounted for.

Source: Scientific Reports

DOI: 10.1038/s41598-026-63474-3

Authors: Muhammad Shazib Hameed, Sobia Zulfiqar, Ghulamullah Saeedi, Usama Bin Khalid, Muhammad Kamran, Shohruh Shuhratovich Shoyimov