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On pairwise comparison matrices that can be made consistent by the modification of a few elements

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  • Sándor Bozóki
  • János Fülöp
  • Attila Poesz

Abstract

Pairwise comparison matrices are often used in Multi-attribute Decision Making for weighting the attributes or for the evaluation of the alternatives with respect to a criteria. Matrices provided by the decision makers are rarely consistent and it is important to index the degree of inconsistency. In the paper, the minimal number of matrix elements by the modification of which the pairwise comparison matrix can be made consistent is examined. From practical point of view, the modification of 1, 2, or, for larger matrices, 3 elements seems to be relevant. These cases are characterized by using the graph representation of the matrices. Empirical examples illustrate that pairwise comparison matrices that can be made consistent by the modification of a few elements are present in the applications. Copyright Springer-Verlag 2011

Suggested Citation

  • Sándor Bozóki & János Fülöp & Attila Poesz, 2011. "On pairwise comparison matrices that can be made consistent by the modification of a few elements," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 19(2), pages 157-175, June.
    • Handle: RePEc:spr:cejnor:v:19:y:2011:i:2:p:157-175
    DOI: 10.1007/s10100-010-0136-9
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    References listed on IDEAS

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    1. S I Gass & S M Standard, 2002. "Characteristics of positive reciprocal matrices in the analytic hierarchy process," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(12), pages 1385-1389, December.
    2. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
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    1. Sándor Bozóki & Linda Dezső & Attila Poesz & József Temesi, 2013. "Analysis of pairwise comparison matrices: an empirical research," Annals of Operations Research, Springer, vol. 211(1), pages 511-528, December.
    2. Bice Cavallo, 2019. "$$\mathcal {G}$$ G -distance and $$\mathcal {G}$$ G -decomposition for improving $$\mathcal {G}$$ G -consistency of a Pairwise Comparison Matrix," Fuzzy Optimization and Decision Making, Springer, vol. 18(1), pages 57-83, March.
    3. Jean-Pierre Magnot & Jiří Mazurek & Viera Cernanova, 2021. "A gradient method for inconsistency reduction of pairwise comparisons matrices," Working Papers hal-03313878, HAL.
    4. Brunelli, Matteo & Fedrizzi, Michele, 2024. "Inconsistency indices for pairwise comparisons and the Pareto dominance principle," European Journal of Operational Research, Elsevier, vol. 312(1), pages 273-282.
    5. Daji Ergu & Gang Kou & János Fülöp & Yong Shi, 2014. "Further Discussions on Induced Bias Matrix Model for the Pair-Wise Comparison Matrix," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 980-993, June.

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