A heuristic method to rectify intransitive judgments in pairwise comparison matrices

Sajid Siraj, Ludmil Mikhailov, John Keane

Research output: Contribution to journalArticlepeer-review


This paper investigates the effects of intransitive judgments on the consistency of pairwise comparison matrices. Statistical evidence regarding the occurrence of intransitive judgements in pairwise matrices of acceptable consistency is gathered by using a Monte-Carlo simulation, which confirms that relatively high percentage of comparison matrices, satisfying Saaty's CR criterion are ordinally inconsistent. It is also shown that ordinal inconsistency does not necessarily decrease in the group aggregation process, in contrast with cardinal inconsistency. A heuristic algorithm is proposed to improve ordinal consistency by identifying and eliminating intransitivities in pairwise comparison matrices. The proposed algorithm generates near-optimal solutions and outperforms other tested approaches with respect to computation time. © 2011 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)420-428
Number of pages8
JournalEuropean Journal of Operational Research
Issue number2
Publication statusPublished - 16 Jan 2012


  • AHP
  • Consistency
  • Decision analysis
  • Heuristics
  • Pairwise comparisons
  • Simulation


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