An Advanced Interval-Valued Fermatean Fuzzy Approach for Aircraft Logistics Optimisation

This study introduces an innovative optimisation paradigm for transportation issues involving high-dimensional uncertainty, specifically targeting aviation logistics. To address the constraints of traditional fuzzy sets in modelling intricate hesitation, we utilise interval-valued Fermatean fuzzy sets (IVFFS), which depict membership and non-membership degrees as intervals constrained by cubic powers, thereby facilitating a more nuanced representation of ambiguity in cost, supply, and demand data. Expanding upon this basis, we provide the mean cube method (MCM), an innovative technique designed to produce an initial basic viable solution specifically for the IVFFS context. The framework is used for three classifications of fuzzy transportation issues: type 1 (uncertain costs), type 2 (uncertain supply and demand), and type 3 (completely uncertain costs, supply, and demand). A comparative investigation of MCM, the mean square method (MSM), and Vogel’s approximation method (VAM), executed in MATLAB, demonstrates that all approaches provide the identical optimum solution. Fuzzy TOPSIS is utilised to identify the optimal approach, with MCM ranked as superior for computing efficiency, solution interpretability, and resilience in uncertain conditions. A case study on aircraft assignment and fuel routing illustrates practical application, while sensitivity analysis verifies stability amid parameter fluctuations, underscoring the framework’s potential for dynamic and intelligent transportation systems.