Efficient vectors in priority setting methodology

Susana Furtado () and Charles R. Johnson ()
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Susana Furtado: Universidade do Porto Rua Dr. Roberto Frias
Charles R. Johnson: College of William and Mary

Annals of Operations Research, 2024, vol. 332, issue 1, No 26, 743-764

Abstract: Abstract The Analytic Hierarchy Process (AHP) is a much discussed method in ranking business alternatives based on empirical and judgemental information. We focus here upon the key component of deducing efficient vectors for a reciprocal matrix of pair-wise comparisons. It has been shown that the entry-wise geometric mean of all columns is efficient for any reciprocal matrix. Here, by combining some new basic observations with some known theory, we (1) give a method for inductively generating large collections of efficient vectors, and (2) show that the entry-wise geometric mean of any collection of distinct columns of a reciprocal matrix is efficient. We study numerically, using different measures, the performance of these geometric means in approximating the reciprocal matrix by a consistent matrix. We conclude that, as a general method to be chosen, independent of the data, the geometric mean of all columns performs well when compared with the geometric mean of proper subsets of columns.

Keywords: Consistent matrix; Decision analysis; Efficient vector; Geometric mean; Reciprocal matrix; 90B50; 91B06; 15A60; 05C20 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10479-023-05771-y

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