A note on a method to ensure rank-order consistency in the analytic hierarchy process

Abstract

Abstract Suppose a decision-maker can specify, with confidence, the rank-order of objects in an AHP pairwise comparison matrix. What he or she is uncertain about is the precise weights that will result. In our experience most decision-makers in this situation feel that the pairwise comparison matrix ought to satisfy some minimal transitive consistency requirements. For instance, if a ij is assessed to be at least 1 (that is w i w j is at least 1) then the transitive product a ik a kj , which also measure w i w j , should also be at least 1. And similarly, if a ij is less than 1, then a ik a kj should also be less than 1. We formalize this idea with a notion termed rank-order consistency and then describe a procedure which allows a decision-maker to guarantee that a matrix is rank-order consistent.