On the proper interpretation and impact of the AHP axiom of independence in single-criterion and multiple-criteria problems

Some authors have proposed that the analytic hierarchy process (AHP) axiom of independence be relaxed to accommodate observations drawn from (a) examples of pairwise comparisons of alternatives in clusters in single-criterion AHP problems and (b) examples of problems in which the criteria have the same underlying measurement and both the achievement of the goal and the alternatives are measured objectively. The authors show that the illustrations given are actually single-criterion problems according to the AHP. Thus the AHP axiom of independence is inapplicable in both situations and therefore not violated. The authors also consider the consequences of failure to distinguish between a criterion as an attribute of alternatives and cluster of alternatives, the two being different in the hierarchic structure. Finally, they discuss transformable problems, which look like multicriteria problems but are actually single-criterion problems, and how failure to recognize this fact may lead to incorrect syntheses and false conclusions.