Aggregation in the Analytic Hierarchy Process: Why weighted geometric mean should be used instead of weighted arithmetic mean

Venue: Seminari room h. 15:00, Polo scientifico-tecnologico Fabio Ferrari - via Sommarive 9 – Trento

• Jana Krejčí - MCI Management Center Innsbruck, Austria

In the Analytic Hierarchy Process (AHP), two approaches for the aggregation of the local priorities of alternatives into the global priorities of alternatives have been proposed – the weighted arithmetic mean and the weighted geometric mean. In the research paper “Krejčí J., Stoklasa, J.: Aggregation in the Analytic Hierarchy Process: Why weighted geometric mean should be used instead of weighted arithmetic mean, Expert Systems with Applications, resubmitted, June 2018.”, we study both approaches to aggregation and identify their strengths and weaknesses. We investigate the focus of the aggregation, the assumptions made on the way, and the effect of different normalizations of local priorities on the resulting global priorities and their ratios. We clearly show the superiority of the weighted geometric mean aggregation over the weighted arithmetic mean aggregation. We also show that a change of the normalization condition for the local priorities of alternatives may result in different ranking when the weighted arithmetic mean aggregation is used for deriving global priorities of alternatives, and we demonstrate that the ranking obtained by the weighted geometric mean aggregation is not normalization dependent. Moreover, we prove that the ratios of global priorities of alternatives obtained by the weighted geometric mean aggregation are invariant under the normalization of local priorities of alternatives and weights of criteria.

Short bio: Jana Krejčí received the Joint Ph.D. degree in Materials, Mechatronics and Systems Engineering from the University of Trento, Italy, and in Economics from the University of Bayreuth, Germany, in 2017. Her research interests include multi-criteria decision-making methods based on pairwise comparisons and their fuzzy extension, constrained interval and fuzzy arithmetic, large-dimensional and incomplete pairwise comparison matrices.