On some convexity properties of the Least Squares Method for pairwise comparisons matrices without the reciprocity condition
The relaxation of the reciprocity condition for pairwise comparisons is revisited from the optimization point of view. We show that some special but not extreme cases of the Least Squares Method are easy to solve as convex optimization problems after suitable nonlinear change of variables. We also give some other, less restrictive conditions under which the convexity of a modified problem can be assured, and the global optimal solution of the original problem found by using local search methods. Mathematical and psychological justifications for the relaxation of the reciprocity condition as well as numerical examples are provided. Copyright Springer Science+Business Media, LLC. 2012
Volume (Year): 54 (2012)
Issue (Month): 4 (December)
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- Gonzalez-Pachon, Jacinto & Romero, Carlos, 2004. "A method for dealing with inconsistencies in pairwise comparisons," European Journal of Operational Research, Elsevier, vol. 158(2), pages 351-361, October.
- Hovanov, Nikolai V. & Kolari, James W. & Sokolov, Mikhail V., 2008. "Deriving weights from general pairwise comparison matrices," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 205-220, March.
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