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When is the condition of order preservation met?

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  • Kułakowski, Konrad
  • Mazurek, Jiří
  • Ramík, Jaroslav
  • Soltys, Michael

Abstract

This article explores the relationship between inconsistency in the pairwise comparisons method and conditions of order preservation. A pairwise comparisons matrix with elements from an alo-group (an Abelian, linearly ordered group) is investigated. This approach allows for a generalization of previous results. Sufficient conditions for order preservation based on the properties of elements of pairwise comparisons matrix are derived. Elucidating numerical examples are presented.

Suggested Citation

  • Kułakowski, Konrad & Mazurek, Jiří & Ramík, Jaroslav & Soltys, Michael, 2019. "When is the condition of order preservation met?," European Journal of Operational Research, Elsevier, vol. 277(1), pages 248-254.
    • Handle: RePEc:eee:ejores:v:277:y:2019:i:1:p:248-254
    DOI: 10.1016/j.ejor.2019.01.046
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    References listed on IDEAS

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    7. Thomas L. Saaty, 2005. "The Analytic Hierarchy and Analytic Network Processes for the Measurement of Intangible Criteria and for Decision-Making," International Series in Operations Research & Management Science, in: Multiple Criteria Decision Analysis: State of the Art Surveys, chapter 0, pages 345-405, Springer.
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    Cited by:

    1. Bice Cavallo, 2019. "Coherent weights for pairwise comparison matrices and a mixed-integer linear programming problem," Journal of Global Optimization, Springer, vol. 75(1), pages 143-161, September.
    2. Fernandes, Rosário & Furtado, Susana, 2022. "Efficiency of the principal eigenvector of some triple perturbed consistent matrices," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1007-1015.
    3. Jaroslav Ramík, 2023. "Deriving priority vector from pairwise comparisons matrix with fuzzy elements by solving optimization problem," OPSEARCH, Springer;Operational Research Society of India, vol. 60(2), pages 1045-1062, June.
    4. Bice Cavallo & Livia D’Apuzzo, 2020. "Relations between coherence conditions and row orders in pairwise comparison matrices," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 637-656, December.
    5. Jiří Mazurek & Konrad Kulakowski, 2020. "Information gap in value propositions of business models of language schools," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 30(2), pages 77-89.

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