Traditional transportation problems focus on a single objective, whereas real-world logistics require multi-objective optimization to consider transportation costs, delivery time, and product deterioration. To handle uncertainty and vagueness, this research presents a FFP (Fermatean fuzzy programming) approach for a nonlinear MOTP (multi-objective transportation problem) under uncertainty, which extends traditional fuzzy numbers by incorporating membership and non-membership values. The problem is transformed using the ( \(\alpha \) , \(\beta \) )-cut technique, converting the nonlinear Fermatean fuzzy transportation problems into interval-valued transportation problems. An accuracy function is then applied to obtain a deterministic equivalent model. Furthermore, supply and demand constraints, modelled as Weibull-distributed probabilistic constraints, are converted into deterministic form using the chance constraint technique. A comparative analysis of solution approaches demonstrates that the proposed FFP method provides superior, more robust results by effectively handling the complex interplay of multiple uncertainties. The study employs fuzzy programming and Fermatean fuzzy programming to determine Pareto-optimal solutions, demonstrating that Fermatean fuzzy programming provides superior results in handling uncertainty. A numerical example illustrates the effectiveness of the proposed model and methodologies in addressing the nonlinearities and uncertainties in transportation problems.
