Misuse of the Axiom of Independence in the Analytic Hierarchy process

Kirti Peniwati
PPM Graduate School of Management
David Hauser
Joseph M. Katz Graduate School of Business
University of Pittsburgh
United States

Publication date: Aug, 1994

Journal: The 3rd International Symposium on the Analytic Hierarchy Process

Publisher: Creative Decisions Foundation

Abstract: 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. We 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. We also consider the consequence of failure to distinguish between a criterion as an attribute of alternatives and a cluster of alternatives, the two being different in the hierarchic structure. Finally, we 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.

Keywords: AHP, Decision making, MCDM, Clustering