Modeling Green 4D Transportation Problem under Fermatean Fuzzy Uncertainty
摘要
Modern transportation systems face increasing pressure to achieve economic efficiency while complying with environmental regulations under highly uncertain conditions. However, most existing models fail to simultaneously capture driving behavior, vehicle–route efficiency interactions, and multi-fuel emission dynamics. This paper proposes a green multi-item four-dimensional transportation problem under a Fermatean fuzzy environment. The proposed model simultaneously integrates route selection, heterogeneous vehicles, fragile products, multi-fuel consumption (diesel, petrol, and CNG), driving behavior, and vehicle–route efficiency interactions within a unified multi-objective optimization framework. The problem is formulated as a multi-objective optimization model aiming to maximize profit while minimizing carbon emissions and transportation time. To capture deep uncertainty and decision-maker hesitation, Fermatean fuzzy sets are employed, offering a more flexible representation than classical fuzzy approaches. A score-based transformation is used to derive a deterministic equivalent model, which is solved using Fuzzy Programming and Two-Phase Programming. Numerical results demonstrate the effectiveness and robustness of the proposed approach in supporting sustainable transportation decisions.