A hybrid method combining three-way decision and DEA game cross-efficiency for procurement mode selection in contract farming

The order procurement mode in contract farming has facilitated the transformation of agriculture from small-scale production to large-scale, intensive production, thus promoting agricultural modernization. However, with the expansion of agricultural operations and increasing complexity of industrial chains, the applicability and flexibility of existing order procurement models face challenges. A single model can no longer cope with the changing production environment. Moreover, few rigorous decision-making tools exist for selecting the appropriate order procurement model. To address these issues, this study proposes a hybrid method combining three-way decision and DEA game cross-efficiency to help agricultural product distribution enterprises in optimizing their selection of order procurement modes. The method involves calculating decision-makers’ weights using cosine similarity based on T-spherical fuzzy sets, constructing a comprehensive evaluation matrix, and combining three-way decision theory with the DEA game cross-efficiency method. It estimates conditional probabilities, constructs a loss function matrix, and determines the probability threshold based on the game cross-efficiency results. Finally, the method's effectiveness is validated through three case studies of Group R, Enterprise H, and Enterprise K, with the comparative experiments further demonstrating the method's accuracy and effectiveness.