A Unit Interpretation of Multi-Criteria Ratios

Abstract

Summary: When AHP 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. First, we look at ratio scales of tangible attributes of objects with well-known measures. Then ratio scales of unknown intangible attributes of objects are analyzed. We discover that natural zero and the 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.