With the rapid development of information, communication and techniques, social network group decision making problems which allow information exchange and communication among experts are more and more common in recent years. How to use social relationships generated by social networks to promote consensus among experts has been becoming a hot topic in the field of group decision making. In this paper, we consider a new type of group decision making problems in which experts will provide his/her interval fuzzy preference relations over alternatives under social network environment and propose a new model to help experts reach consensus. In the proposed model, we first define the individual consensus measure and the group consensus measure, and then use a network partition algorithm to detect sub-networks of experts, based on which the leadership of experts can be identified. Afterwards, by considering the leadership and the bounded confidence levels of experts, a new feedback mechanism which can provide acceptable advice to experts who need to modify their opinions is devised and a consensus reaching algorithm is further developed. To demonstrate the performance of the proposed consensus model and algorithm, a hypothetical application and some simulation analysis are provided eventually.