A Sustainable Multi-objective Fixed Charge 4-Dimensional Triangular Fermatean Hesitant Fuzzy Transportation Framework

In this article, we first propose triangular fermatean hesitant fuzzy numbers (Tr-FHFN) as a triangular form of the dual hesitant fermatean fuzzy set (DHFFS) to address uncertainty embedded in real-world optimization issues. In order to address sustainability in transportation systems by integrating environmental, economic, and social assets in a single framework, we devised a sustainable fixed charge 4D transportation system that optimizes the transportation cost (TC) and carbon emission (CE). Additionally, we also used fuzzy programming (FP), and weighted sum technique (WST) which helps in obtaining the model's optimal answer. The significance of the proposed model is further elaborated on through the numerical computations. Analysis of the results obtained using FP and WST also carried out. Finally, conclusions are drawn with future prospects.