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

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 the experience of the authors, most decision-makers in this stuation feel that the pairwise comparison matrix ought to satisfy some minimal transitive consistency requirements. For instance, if aij is assessed to be at least 1 (that is wi/wj is at least 1) then the transitive product aikakj, which also measure wi/wj, should also be at least 1. And similarly, if aij is less than 1, then aikakj should also be less than 1. This paper formalizes this idea with a notion termed rank-order consistency and then describes a procedure which allows a decision-maker to guarantee that a matrix is rank-order consistent.