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 fuzz...