This paper proposes a novel multi-criteria decision making method under uncertainty that combines the Analytic Hierarchy Process (AHP) with the belief function theory. Our method, named belief AHP, allows the expert to express incomplete and imprecise information about groups of alternatives instead of single ones. On the other hand and in order to judge the importance of criteria, he can also present his opinions on groups of criteria. Then, the uncertainty will be taken into account in the final decision. Finally, another purpose of this paper is also to solve a real application problem which deals with the PVC life cycle assessment.