This research mainly focuses on presenting an innovative study of a multi-stage multi-objective fixed-charge solid transportation problem (MMFSTP) with a green supply chain network system under an intuitionistic fuzzy environment. The most controversial issue in recent years is that greenhouse gas emissions such as carbon dioxide, methane, etc. induce air pollution and global warming, thus motivating us to formulate the proposed research. In real-world situations the parameters of MMFSTP via a green supply chain network system usually have unknown quantities, and thus we assume trapezoidal intuitionistic fuzzy numbers to accommodate them and then employ the expected value operator to convert intuitionistic fuzzy MMFSTP into deterministic MMFSTP. Next, the methodologies are constructed to solve the deterministic MMFSTP by weighted Tchebycheff metrics programming and min-max goal programming, which provide Pareto-optimal solutions. A comparison is then drawn between the Pareto-optimal solutions that are extracted from the programming, and thereafter a procedure is performed to analyze the sensitivity analysis of the target values in the min–max goal programming. Finally, we incorporate an application example connected with a real-life industrial problem to display the feasibility and potentiality of the proposed model. Conclusions about the findings and future study directions are also offered.

这项研究主要集中于在直觉模糊环境下，利用绿色供应链网络系统对多阶段多目标固定收费固体运输问题（MMFSTP）进行创新研究。近年来最有争议的问题是二氧化碳，甲烷等温室气体的排放会导致空气污染和全球变暖，因此促使我们制定了拟议的研究。在现实世界中，通过绿色供应链网络系统的MMFSTP参数通常数量未知，因此我们假设梯形直觉模糊数可以容纳它们，然后使用期望值算子将直觉模糊MMFSTP转换为确定性MMFSTP。下一个，通过加权Tchebycheff度量编程和最小最大目标编程来构造确定性MMFSTP的方法，从而提供帕累托最优解。然后从编程中提取的帕累托最优解之间进行比较，然后执行一个过程来分析最小-最大目标编程中目标值的敏感性分析。最后，我们结合一个与实际工业问题相关的应用示例，以展示所提出模型的可行性和潜力。还提供了有关发现和未来研究方向的结论。然后执行一个程序来分析最小-最大目标编程中目标值的敏感性分析。最后，我们结合一个与实际工业问题相关的应用示例，以展示所提出模型的可行性和潜力。还提供了有关发现和未来研究方向的结论。然后执行一个程序来分析最小-最大目标编程中目标值的敏感性分析。最后，我们结合一个与实际工业问题相关的应用示例，以展示所提出模型的可行性和潜力。还提供了有关发现和未来研究方向的结论。