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ABSTRACTWhen Analytic Hierarchy Process ratios are normalized to sum to unity, the unit of measure becomes obscure. This paper investigates this obscurity and whether ratio measurement is possible when there is no prior knowledge of the measurement unit. Initially, we look at ratio scales of tangible attributes of objects with well‐known measures. Then, ratio scales of unknown intangible attributes of objects are analysed. We discover that natural zero and a specific unit of measure are not necessarily used explicitly in deriving ratio scale measures. Nevertheless, the derived scale does have a derived unit of measurement. We conclude that although composite multi‐criteria answers are possible in ratio form, it is important to know that a unit of measure exists if ambiguities are to be avoided. Copyright © 2011 John Wiley & Sons, Ltd.

AbstractIn the analytic hierarchy process, it is often thought that rank reversals cannot occur in a single‐criterion problem. This paper demonstrates that if it is necessary to cluster items under a single criterion, such reversals are possible. The reversals occur prior to aggregating across clusters and are caused by a failure to make reference to the alternatives when performing criteria comparisons. Rank reversals, however, are only a symptom of the problem. The real problem is a failure to calibrate global weights to a common scale which spans different clusters. Even in the absence of reversals, aggregated weights from the AHP's relative mode of measurement can fail to maintain composite ratio relationships.

ABSTRACTIn an earlier paper [11], the problems of rank reversals and invalid composite priorities in AHP were addressed by modifications to the AHP procedure. That solution was subsequently criticized [5]. In this paper, we rebut these criticisms, and we show how rank reversals in AHP can arise merely from the process of normalizing local priorities.