Pentagonal fuzzy fractional three-stage sustainable transportation network problem incorporating extension principle

This study presents a framework for addressing the fuzzy fractional three-stage transportation network (FFTSTN) in the context of sustainable conveyance. The proposed model considers the transportation costs and profits involved in moving goods from manufacturers to storage godowns, storage godowns to distributors, and distributors to consumers. The primary aim of this study is to mitigate transportation expenses and assess transportation's environmental viability through reducing emissions. A generalized pentagonal fuzzy number (GPFN) is employed to address the uncertainty of parameters of the three-stage transportation network. The study established a methodology to explore solutions for the FFTSTN model without de-fuzzifying GPFNs. Additionally, it explored the economic sustainability and future transportation prospects using the extension principle to solve the proposed FFTSTN system. This solution approach considers the nonlinearity of the objective function by utilizing the Charnes-Cooper transformation technique for the problem. A numerical example shows applicability, validity, and comparison between the compromise solutions.