A Solution of Mathematical Multi-Objective Green Transportation Problems Under the Fermatean Fuzzy Environment

Abstract

This paper presents a mathematical framework for solving green Transportation Problem (TP) under uncertainty using Fermatean Fuzzy Parameters (FFP). Focusing on a Multi-Objective Transportation Problem (MOTP), the model aims to simultaneously minimize transportation cost, travel time, and carbon emissions—key metrics in sustainable logistics. All parameters, including costs, supply, and demand, are treated as Fermatean fuzzy to capture real-world ambiguity and uncertainty better. We introduce a New Fermatean Fuzzy Score Function (NFFSF) that converts fuzzy values into crisp equivalents to handle these fuzzy parameters. A Fermatean Fuzzy Programming Approach (FFPA) is applied to derive compromise solutions that balance economic efficiency with environmental responsibility. A numerical example illustrates the practicality and effectiveness of the proposed method in supporting eco-friendly and optimized transportation planning. This approach provides a robust decision-making tool for achieving sustainability goals in complex and uncertain transportation environments.