A minimum adjustment cost feedback mechanism based consensus model for group decision making under social network with distributed linguistic trust

A theoretical feedback mechanism framework to model consensus in social network group decision making (SN-GDM) is proposed with following two main components: (1) the modelling of trust relationship with linguistic information; and (2) the minimum adjustment cost feedback mechanism. To do so, a distributed linguistic trust decision making space is defined, which includes the novel concepts of distributed linguistic trust functions, expectation degree, uncertainty degrees and ranking method. Then, a social network analysis (SNA) methodology is developed to represent and model trust relationship between a networked group, and the trust in-degree centrality indexes are calculated to assign an importance degree to the associated user. To identify the inconsistent users, three levels of consensus degree with distributed linguistic trust functions are calculated. Then, a novel feedback mechanism is activated to generate recommendation advices for the inconsistent users to increase the group consensus degree. Its novelty is that it produces the boundary feedback parameter based on the minimum adjustment cost optimisation model. Therefore, the inconsistent users are able to reach the threshold value of group consensus incurring a minimum modification of their opinions or adjustment cost, which provides the optimum balance between group consensus and individual independence. Finally, after consensus has been achieved, a ranking order relation for distributed linguistic trust functions is constructed to select the most appropriate alternative of consensus.