Uncertainty and rank order in the analytic hierarchy process

The Analytic Hierarchy Process uses paired comparisons to derive a scale of relative importance for alternatives. We investigate the effect of uncertainty in judgment on the stability of the rank order of alternatives. The uncertainty experienced by decision makers in making comparisons is measured by associating with each judgment an interval of numerical values. The approach leads to estimating the probability that an alternative or project exchanges rank with other projects. These probabilities are then used to calculate the probability that project would change rank at all. We combine the priority of importance of each project with the probability that it does not change rank, to obtain the final ranking.