In this paper, a novel consensus model for group decision making based on discrete fuzzy numbers is proposed. The experts express their preferences over the alternatives by means of the so-called subjective linguistic preference relations, which allow a greater flexibility of the experts' opinions. The model consisting of a consensus and a selection phases is able to achieve the consensus without any loss of information and without imposing to the experts any drastic change on their initial opinions. Finally, a group decision making problem based on this model is presented.