A joint feedback strategy for consensus in large-scale group decision making under social network

Nowadays, large-scale group decision making (LSGDM) has become a hot topic and brought new challenges for the decision makers. This article proposes a framework of joint feedback strategy to help large-scale group decision makers to reach an agreement by combing social network context and feedback behavior. Firstly, the social network of large-scale group decision makers is explored to study the trust relationship, and it is used to assign weights associated to decision makers. And the recommendation advice can be generated by trust relationship using as reliable resource to aggregate group opinions to a collective one. Secondly, the recommendation advice is embedded to the feedback mechanism in LSGDM, and a joint feedback strategy is proposed based on harmony degree to help the multiple non-consensus decision makers modify their preferences to improve the efficiency of consensus achievement. In detail, this article builds two optimization models with the aim of maximum harmony degree: (1) one is with consistent feedback behaviour; (2) the other is with different feedback behaviour. At last, a numerical and a comparison analysis are provided to show the validity of joint feedback strategy with different feedback behaviors.