The concept of green supply chain management (GSCM) describes how to reduce the negative impact of the supply chain on the environment while balancing the economic and social benefits of a company being in the supply chain. Selecting the optimal multi-dimensional GSCM scheme, a typical multi-criteria decision-making (MCDM) problem, is a crucial step in implementing the GSCM concept. Therefore, this paper constructs a multi-dimensional GSCM index system for the comprehensive analysis of the important influencing factors of GSCM. Then, cross-entropy combining the interval type-2 trapezoidal fuzzy set (IT2TFS) is adopted to determine the weight distribution of GSCM indices, and a hybrid MCDM method integrating the IT2TFS prospect–regret method is proposed to analyze the psychological behaviors of decision makers who are selecting the best GSCM scheme. Moreover, the case study, comparative analysis, and sensitivity analysis are presented to verify the effectiveness and reasonableness of the proposed MCDM method. The results affirm the validity of the proposed MCDM method, with A₄ identified as the optimal GSCM scheme, demonstrating its effectiveness and applicability in MCDM problems.