Energy internet project evaluation in circular economy practices: A novel multi-criteria decision-making framework with flexible linguistic expressions based on multi-granularity cloud-rough set

Energy internet (EI) serves as a practical platform for implementing the principles of the circular economy. As the process of realizing the transformation of industrial systems to a sustainable circular economy accelerates, the importance of evaluating and selecting the most effective EI projects becomes increasingly apparent. This paper proposes a new multi-criteria decision-making (MCDM) framework based on the multi-granularity cloud-rough set (MGCRS) and flexible linguistic expressions (FLEs) to evaluate and select different EI projects. Firstly, a comprehensive index system is established from three aspects including grid technology, green energy, and composite benefits. Secondly, FLE is used to express experts’ preferences and a transformation method converting discrete FLEs into continuous cloud information is proposed. To select the best EI project, the optimistic MGCRS and pessimistic MGCRS over two universes are presented to deal with the continuous cloud information in the decision-making process. Furthermore, the comprehensive multi-granularity lower approximation and upper approximation based on the cloud model are proposed to rank different EI projects. Finally, a case study of China's Beijing–Tianjin–Hebei region is analyzed to illustrate the proposed model, and the simulation and comparative analyses are provided to demonstrate the effectiveness of the proposed framework.