Using the three-way matrix for AHP-group decision-making

The Analytic Hierarchy Process (AHP) is one of the most well-known and used multi-criteria methods in the field of decision problems. In many situations, the decision is not up to a single person but involves multiple decision-makers with different preferences with respect to the various elements of the problem. Applying a traditional AHP with certain preference aggregation mechanisms, the procedure is very burdened by the many pairwise comparison matrices due to the number of decision-makers. The aim of this paper is to summarize the problem of representing the different preferences between the criteria and the alternatives, for the various decision makers using the three-way data matrix. This matrix allows us to examine, in a contemporary and global manner, the preferences of several decision-makers in the decision-making context. Three-way principal component models can be used to treat the three-way matrix, particularly for the derivation of AHP priorities.