Optimal group selection model for large-scale group decision making

Abstract

Research on large-scale group decision making (LSGDM) has generally focused on clustering and reaching a consensus. Often, participants (or decision makers) are unwilling to share their consensus or revise their preferences, which leads to the loss of time and money and even reduces the efficiency of decision making. Accordingly, in LSGDM, an optimal group derived from a large number of participants could improve the decision-making efficiency and reduce time consumption. In this paper, we investigate a model to select the optimal group for LSGDM with multiplicative preference relations. Notably, for individual and group preference relations, we define an individual logarithmic square compatibility measure and a group logarithmic square compatibility measure, respectively. Some properties associated with the individual logarithmic square compatibility measure and group logarithmic square compatibility measure are addressed. For a large number of preferences in LSGDM, the redundant preferences and optimal group are distinguished based on an optimal group selection model using the optimal participant weights obtained by minimizing the group logarithmic square compatibility model. Then, we demonstrate that the model is a convex quadratic programming problem. Moreover, the conditions for the existence of an optimal solution and the conditions for redundant preference relations in the group logarithmic square compatibility model are provided. In this context, the proposed model is verified to effectively identify the optimal group.