In this study, we developed a comprehensive mathematical model of a multi-objective multi-commodity solid transportation problem (MOMCSTP) incorporating fuzzy parameters, represented as trapezoidal fuzzy numbers. The proposed model is initially formulated in a fuzzy environment and subsequently transformed into a crisp form using the \(\alpha\:-\) cut approach. This transformation facilitates the application of three distinct optimization techniques, namely, the fuzzy programming approach (FPA), the interactive fuzzy goal programming approach (IFGPA), and the fermatean fuzzy programming approach (FFPA), applied to both integer and non-integer cases. A detailed case study is provided to demonstrate the reliability and validity of the proposed problem. The comparison of results reveals that while FPA and IFGPA yield identical solutions, FFPA emerges as the most reliable and practical method, delivering superior solutions to the MOMCSTP. This study contributed to and enhanced the effectiveness of FFPA in addressing the complexities of fuzzy parameter-based optimization to unfold solid transportation problems. Practical and managerial implications are discussed.
