Consequences of uncertainty in the analytic hierarchy process: A simulation approach

A methodology for the propagation of uncertainty in the analytic hierarchy process is described. The sole source of the uncertainty is assumed to lie in the elements of the preference matrices. The uncertainty in decision alternative rankings and the probability of a rank reversal as functions of the number of alternatives and hierarchy depth are examined. Ranking uncertainty is found to decrease as the number of alternatives or the depth of the hierarchy is increased. The observed behaviour of ranking uncertainty is partially explained using the central limit theorem.