Skyline queries have gained much attention in the last decade and are proved to be valuable for multi-criteria decision making. When computing the skyline, two scenarios may occur: either (i) a huge number of skyline or (ii) a small number of returned objects which could be insufficient for the user needs. In this paper, we tackle the second problem and propose an approach to deal with it and to make the skyline more permissive. A new fuzzy variant of dominance relationship is then introduced. Furthermore, an efficient algorithm to compute the relaxed skyline is proposed. Extensive experiments are conducted to demonstrate the effectiveness of our approach and the performance of the proposed algorithm.