Consensus reaching with the externality effect of social network for three-way group decisions

Abstract

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.