Three-way group decisions provide an efficient method to settle complex and high risk decision-making problems. To obtain reasonable decision results that satisfy different backgrounds and knowledge of decision makers, it is necessary to design a proper consensus reaching process (CRP) for loss functions of decision-theoretic rough sets (DTRSs). Unlike existing researches, this paper not only extends the group relationship among decision makers to the social network, but also considers the externality of social trust network in group decision making. In light of this idea, we design a new CRP with the externality of social network for three-way group decisions. In the CRP, the adjustment of a decision maker who is persuaded by the moderator can influence other decision makers to accordingly adjust evaluations. Thus, by using the linkage externality influence among decision makers, we establish a two-stage mixed 0–1 linear optimization consensus model for the determination of loss functions of DTRSs. Then, based on Bayesian decision procedure, we construct a complete decision procedure for three-way group decisions with social network. Finally, we apply our proposed method to assess desert locust invasion areas and verify its validity.

三方小组决策提供了一种解决复杂和高风险决策问题的有效方法。为了获得满足不同背景和决策者知识的合理决策结果，有必要针对决策理论粗糙集（DTRS）的损失函数设计适当的共识达成过程（CRP）。与现有研究不同的是，本文不仅将决策者之间的群体关系扩展到社交网络，而且考虑了社交信任网络在群体决策中的外部性。根据这个想法，我们设计了一种新的CRP，它具有社交网络的外部性，可以进行三方小组决策。在CRP中，主持人说服的决策者调整可能会影响其他决策者，从而相应地调整评估。从而，通过利用决策者之间的联系外部性影响，我们建立了确定DTRS损失函数的两阶段混合0–1线性优化共识模型。然后，基于贝叶斯决策过程，利用社交网络构造了一套完整的三路群体决策决策过程。最后，我们将我们提出的方法用于评估沙漠蝗虫入侵地区并验证其有效性。