Papers

Comparison of eigenvalue, logarithmic least squares and least squares methods in estimating ratios

Author(s)
Thomas Saaty
Joseph M. Katz Graduate School of Business
University of Pittsburgh
United States
Luis Vargas
Joseph M. Katz Graduate School of Business
University of Pittsburgh
United States

Publication date: Jan, 1984

Journal: Mathematical modelling
Vol.: 5- Issue: 5- Pages: 309-324

Abstract: Three methods—the eigenvalue, logarithmic least squares, and least squares methods—used to derive estimates of ratio scales from a positive reciprocal matrix are analyzed. The criteria for comparison are the measurement of consistency, dual solutions, and rank preservation. It is shown that the eigenvalue procedure, which is metric-free, leads to a structural index for measuring inconsistency, has two separate dual interpretations and is the only method that guarantees rank preservation under inconsistency conditions.

Keywords: Eigenvector, Logarithmic least squares, Least squares, Consistency

URL: https://doi.org/10.1016/0270-0255(84)90008-3