Computing a consistent approximation to a generalized pairwise comparisonsmatrix

This paper presents an algorithm for computing a consistent approximation t o a generalized pairwise comparisons matrix (that is, without the reciproci ty property or even Is on the main diagonal). The algorithm is based on a l ogarithmic transformation of the generalized pairwise comparisons matrix in to a linear space with the Euclidean metric. It uses both the row and (reci procals of) column geometric means and is thus a generalization of the ordi nary geometric means method. The resulting approximation is not only consis tent, but also closest to the original matrix, i.e., deviates least from an expert's original judgments. The computational complexity of the algorithm is O(n(2)). (C) 1999 Elsevier Science Ltd. All rights reserved.