Multi-Criteria Ratios: What is the Unit?

When 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.