Abstract: Fuzzy and multi-attribute conditions exist widely in the decision-making environments. It has been research interesttomake the two complex conditions be a simple and distinct relation, the theory about which, however, is not satisfactory. In this paper, the properties of consistent matrix under fuzzy preferences are studied, and two necessary and sufficient conditions for the equivalence between fuzzy consistent matrix and fuzzy compensation matrix are proved. The multi-attribute group decision-making method under fuzzy preferences is proposed based on the analysis. The effectiveness of the method is shown with a practical example