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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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    1. Bana e Costa, Carlos A. & Vansnick, Jean-Claude, 2008. "A critical analysis of the eigenvalue method used to derive priorities in AHP," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1422-1428, June.
    2. Ho, William & Ma, Xin, 2018. "The state-of-the-art integrations and applications of the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 267(2), pages 399-414.
    3. Fedrizzi, Michele & Giove, Silvio, 2007. "Incomplete pairwise comparison and consistency optimization," European Journal of Operational Research, Elsevier, vol. 183(1), pages 303-313, November.
    4. J. Fülöp & W. Koczkodaj & S. Szarek, 2012. "On some convexity properties of the Least Squares Method for pairwise comparisons matrices without the reciprocity condition," Journal of Global Optimization, Springer, vol. 54(4), pages 689-706, December.
    5. 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.
    6. Liberatore, Matthew J. & Nydick, Robert L., 2008. "The analytic hierarchy process in medical and health care decision making: A literature review," European Journal of Operational Research, Elsevier, vol. 189(1), pages 194-207, August.
    7. Martin Gavalec & Jaroslav Ramík & Karel Zimmermann, 2015. "Decision Making and Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, edition 127, number 978-3-319-08323-0, July.
    8. Konrad Kułakowski & Katarzyna Grobler-Dębska & Jarosław Wąs, 2015. "Heuristic rating estimation: geometric approach," Journal of Global Optimization, Springer, vol. 62(3), pages 529-543, July.
    9. Ho, William, 2008. "Integrated analytic hierarchy process and its applications - A literature review," European Journal of Operational Research, Elsevier, vol. 186(1), pages 211-228, April.
    10. Vaidya, Omkarprasad S. & Kumar, Sushil, 2006. "Analytic hierarchy process: An overview of applications," European Journal of Operational Research, Elsevier, vol. 169(1), pages 1-29, February.
    11. Martin Gavalec & Jaroslav Ramík & Karel Zimmermann, 2015. "Pairwise Comparison Matrices in Decision Making," Lecture Notes in Economics and Mathematical Systems, in: Decision Making and Optimization, edition 127, chapter 0, pages 29-90, Springer.
    12. James E. Smith & Detlof von Winterfeldt, 2004. "Anniversary Article: Decision Analysis in Management Science," Management Science, INFORMS, vol. 50(5), pages 561-574, May.
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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. 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.
    3. 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.
    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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