An Interval-Valued Fermatean Neutrosophic Framework for Sustainable Transportation Under Uncertainty

Transportation planning is facing heightened complexity because the dynamic parameters influenced by globalization and unpredictable technological disruptions. Traditional models are not capable to handle interval-based uncertainties related to supply, demand, and costs, especially as the scale of suppliers and customers expands. To bridge this gap, the current study develops a hybrid framework using interval-valued Fermatean neutrosophic fuzzy numbers (IVFNFNs) in interval data–based transportation problems. Unlike classical fuzzy or neutrosophic techniques, IVFNFNs combine Fermatean fuzzy sets’ ability to capture higher-order uncertainties with interval-valued neutrosophic logic’s granular representation of ambiguity, offering unmatched flexibility in modeling incomplete, inconsistent, and indeterminate transportation data. The major contributions of this study are threefold. First, IVFNNs utilize cubic constraints that contribute tighter bounds on feasible solutions compared with Pythagorean or intuitionistic fuzzy sets, reducing solution space overestimation. Second, we derive a novel scoring function that preserves interval uncertainty through endpoint-weighted aggregating while maintaining consistency with Fermatean constraints, enabling direct integration with classical transportation algorithms. The practical superiority of our methodology is demonstrated through extensive numerical analysis. When applied to large-scale transportation networks, IVFNNs achieve 15.3% lower average costs than interval-valued intuitionistic models under identical uncertainty conditions while completely eliminating constraint violations in unbalanced scenarios. By maintaining cost efficiency with environmental and social sustainability, our method provides actionable comprehension for supply chain managers and policymakers.