The relationships among group decision making units based on partial ordered set

Abstract

Enterprise competitiveness has grown exceedingly fierce in recent years as a result of big data and advancement in information technologies. Enterprise competition has evolved from basic competition between the two firms to complex competition among enterprises. Furthermore, epidemics and wars are likely to turn the rivalry between firms into a large-scale game between countries. Traditional data envelopment analysis (DEA) has several limitations when it comes to finding complicated relationships among decision making units (DMUs). The DEA method, which is based on partially ordered set theory, is the first to establish a partial order relationship between two DMUs. However, this method cannot find the relationship between decision making groups (DMGs), and the model has not yet been extended to the Banker, Charnes and Cooper (BCC) model with variable returns to scale. This paper proposes a theory for establishing the partial order relationship of DMGs using the DEA method, and it accomplishes the goal of quantifying and visualizing the relationship of the DMGs by providing algorithms and visual display techniques. The associated findings not only disclose the reasons for DMUs’ ineffectiveness, but also explain the complicated envelope, competition, and cooperation among DMUs. More crucially, the method can assess the importance of DMUs and DMGs, and also evaluate the value of cooperation, competition, and learning of decision group. At the same time, this theory can provide practical and diverse theoretical support for the gradual projection improvement and cooperative game of DMUs and thus has immense practical value.