PERTURBATION ANALYSIS OF THE ANALYTIC HIERARCHY DECISION METHOD

The input set for the Analytic Hierarchy Process consists of the integers less than ten and their reciprocals. A perturbation in the input may cause significant change in the output vector, particularly when the dimension of the input matrix is small (n less-than-or-equal-to 4) and the inputs are close together. We examine that change using numerical computational schemes. The cardinal values of the output vector are seen to suffer significant perturbation due to small integral changes on all the inputs. Ordinal perturbations are less pronounced and can be better quantified by a numerical scheme. Known indices of consistency provide an indicator of truly poor input data. For an unskilled modeler, they can provide a false sense of assurance, but these consistency measures do not protect the modeler from consistently inaccurate inputs.