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Central European Journal of Operations Research

, Volume 19, Issue 4, pp 439–444 | Cite as

A simplified implementation of the least squares solution for pairwise comparisons matrices

  • Marcin Anholcer
  • Volodymyr Babiy
  • Sándor Bozóki
  • Waldemar W. KoczkodajEmail author
Original Paper

Abstract

This is a follow up to “Solution of the least squares method problem of pairwise comparisons matrix” by Bozóki published by this journal in 2008. Familiarity with this paper is essential and assumed. For lower inconsistency and decreased accuracy, our proposed solutions run in seconds instead of days. As such, they may be useful for researchers willing to use the least squares method instead of the geometric means method.

Keywords

Pairwise comparison matrix Least squares method Inconsistency analysis Generalized reduced gradient algorithm Optimization 

Mathematics Subject Classification (2000)

05C78 

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References

  1. Bozóki S (2008) Solution of the least squares method problem of pairwise comparisons matrices. Central Eur J Oper Res 16: 345–358CrossRefGoogle Scholar
  2. Bozóki S, Rapcsák T (2008) On Saaty’s and Koczkodaj’s inconsistencies of pairwise comparison matrices. J Glob Optim 42(2): 157–175CrossRefGoogle Scholar
  3. Koczkodaj WW (1993) A New definition of consistency of pairwise comparisons. Math Comput Model 18(7): 79–84CrossRefGoogle Scholar
  4. Lasdon LS, Warren AD, Jain A, Ratner M (1978) Design and testing of a generalized reduced gradient code for nonlinear programming. ACM Trans Math Software 4: 34–50CrossRefGoogle Scholar
  5. Lasdon LS, Warren AD (1997) GRG2 user’s guide (Posted on the Internet), p. 50. http://www.cadfamily.com/download/CAE/isight8/Grg2User.doc; http://www.docstoc.com/docs/2137299/GRG2-user-guide. Accessed 11 Jan 2010

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Marcin Anholcer
    • 1
  • Volodymyr Babiy
    • 2
  • Sándor Bozóki
    • 3
  • Waldemar W. Koczkodaj
    • 4
    Email author
  1. 1.Department of Operations ResearchPoznań University of EconomicsPoznańPoland
  2. 2.Department of Computer ScienceMcMaster UniversityHamiltonCanada
  3. 3.Laboratory on Engineering and Management Intelligence, Research Group of Operations Research and Decision SystemsComputer and Automation Research Institute, Hungarian Academy of SciencesBudapestHungary
  4. 4.Department of Computer ScienceLaurentian UniversitySudburyCanada

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