The problem of different pairwise comparisons scales in the AHP framework

Abstract

In pairwise comparisons, several scales are used to compare objects. Perhaps the most known is Saaty’s fundamental scale for the AHP/ANP from 1 to 9 (with reciprocals), but other scales with 3, 5 or 10 items are also used in practice. Since the AHP/ANP is scale invariant, the following problem arises: for example, a preference of one object over other object expressed by the value 2 means something else for the scale from 1 to 3 (it expresses the medium preference) and the scale from 1 to 100 (in this case the preference is almost negligible). Therefore, the need of a normalization for pairwise comparison scales arises. The aim of the article is to propose a suitable transformation of a general linear scale for pairwise comparisons to a unit real interval that preserves several natural and desirable properties.