Belief AHP Method — AHP Method with the Belief Function Framework

In this paper, the analytic hierarchy process (AHP) method is extended to an uncertain environment where the uncertainty is represented by belief functions as interpreted in the transferable belief model (TBM). Our proposed approach, called belief AHP, is developed to help the decision maker to determine what the best alternatives are, considering multiple conflicting criteria where both alternatives and criteria may be soiled with imperfection. The Belief AHP method aims at comparing subsets of criteria and groups of alternatives in order to reduce the pair-wise comparisons number. Furthermore, to handle uncertainty that may appear in the comparison procedure, we use basic belief assignments (BBA) instead of exact ratios to elicitate expert preferences. Finally, to illustrate the feasibility of our approach and to judge its performances, we have applied our proposed method on a real application problem: we have considered the polyvinyl chloride (PVC) life cycle assessment especially the end of life phase.