Normalisation and rank reversals in the additive analytic hierarchy process: a new analysis

We provide an explicit derivation of a new aggregation rule that naturally incorporates the relative strength of normalisation with respect to different criteria. The proposed aggregation procedure avoids unwanted rank reversals in the additive Analytic Hierarchy Process. In the case of absolute measure, the strength of normalisation is manifested by the priority vector's norm that can be interpreted as the unit of measure. However, when we have only relative judgements, norms are unknown and thus the decision maker has to estimate the relative strength of normalisation. Simultaneously, the new aggregation mechanism allows acceptable rank reversals if imperfections of human behaviour are recognised.