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Highlights • The results of aggregation by weighted arithmetic mean are normalization-dependent. • Weighted arithmetic mean aggregation fails to reflect preference information well. • Serious problems caused by the arithmetic mean aggregation shown on examples. • Theorems claiming the superiority of geometric mean aggregation in AHP presented. • Weighted geometric mean recommended for aggregation of local priorities in AHP. Abstract 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. [ABSTRACT FROM AUTHOR]

The transformations between multiplicatively and additively reciprocal fuzzy pairwise comparison matrices are dealt with, and formulas for obtaining multiplicative fuzzy priorities from additively reciprocal fuzzy pairwise comparison matrices are proposed in this paper. The formulas are based on the concept of constrained fuzzy arithmetic and preserve the additive reciprocity of pairwise comparisons. Further, the consistency issue is approached in the paper; the consistency check is employed directly in the formulas for obtaining multiplicative fuzzy priorities of objects both from multiplicatively and additively reciprocal fuzzy pairwise comparison matrices. Two definitions of consistency based on transitivity are employed in this paper-the traditional additive/multiplicative transitivity and the weak consistency. However, also several other transitivity conditions are discussed in this context. Finally, the proposed formulas for obtaining multiplicative fuzzy priorities from an additively reciprocal fuzzy pairwise comparison matrix and the formulas with employed consistency check are applied in an illustrative example. Triangular fuzzy numbers are used for the fuzzy extension in this paper. However, all the formulas can be modified easily to be applied on intervals, trapezoidal fuzzy numbers or any other fuzzy numbers given by $$\alpha $$ -cuts. [ABSTRACT FROM AUTHOR]