A1 Journal article (refereed), original research

Aggregation in the analytic hierarchy process: Why weighted geometric mean should be used instead of weighted arithmetic mean

Publication Details
Authors: Krejčí Jana, Stoklasa Jan
Publisher: Elsevier
Publication year: 2018
Language: English
Related Journal or Series Information: Expert Systems with Applications
Journal acronym: ESWA
Volume number: 114
Start page: 97
End page: 106
Number of pages: 10
ISSN: 0957-4174
eISSN: 1873-6793
JUFO-Level of this publication: 1
Open Access: Not an Open Access publication


The main focus of this paper is the aggregation of local priorities into global priorities in the Analytic Hierarchy Process (AHP) method. We study two most frequently used aggregation approaches - the weighted arithmetic and weighted geometric means - 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 in AHP for the purpose of deriving global priorities of alternatives. We also contribute to the literature on rank reversal in AHP. In particular, we 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. We also propose three alternative approaches to aggregating preference information contained in local pairwise comparison matrices of alternatives into a global consistent pairwise comparison matrix of alternatives and prove their equivalence.

Last updated on 2019-13-03 at 12:00