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We are observing more often extreme climate incidents because of global warming. There is a dire requirement for governments, enterprises, the overall population, and academics to take facilitated activities so as to handle the difficulties forced by environmental change. The most important strategic issue is to design an effective and environmentally concerned logistics system as transportation is one of the fundamental reasons for carbon emanations. Having this goal and mentioned highly important contributions in the field, this article introduces an unprecedented integrated mathematical model for a green solid transportation system with dwell time to execute the carbon tax, cap, and offset regulation. Due to market fluctuations, the supply and demand parameters are not always of crisp nature. Hence, a twofold (type-2 intuitionistic) uncertainty is incorporated in this article to provide a realistic transportation system …