Skyline queries were recently expanded to group decision making to meet complex real-life needs encountered in many modern application domains that does not only require analyzing individual points but also groups of points. Group skyline aims at retrieving groups that are not dominated by any other group of the same size in the sense of a group-dominance relationship. It may often happens that this kind of dominance leads to only a small number of non-dominated groups which could be insufficient for the decision maker. In this paper, we propose to extend group skyline dominance by making it more demanding so that several groups leave incomparable. Then, the original group skyline will be enlarged by some interesting groups that are not much dominated by any other group. The key element of this relaxation is a particular fuzzy preference relation, named ”much preferred”, conveniently chosen. Furthermore, algorithms to compute the relaxed group sky-line are proposed. Finally, a set of experiments are conducted on real, synthetic and generated data. Such experiments show that our proposal can really improve the decision process and satisfy user queries, insure reliability and decision quality.