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Inconsistency indices for pairwise comparison matrices: a numerical study

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  • Matteo Brunelli
  • Luisa Canal
  • Michele Fedrizzi

Abstract

Evaluating the level of inconsistency of pairwise comparisons is often a crucial step in multi criteria decision analysis. Several inconsistency indices have been proposed in the literature to estimate the deviation of expert’s judgments from a situation of full consistency. This paper surveys and analyzes ten indices from the numerical point of view. Specifically, we investigate degrees of agreement between them to check how similar they are. Results show a wide range of behaviors, ranging from very strong to very weak degrees of agreement. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Matteo Brunelli & Luisa Canal & Michele Fedrizzi, 2013. "Inconsistency indices for pairwise comparison matrices: a numerical study," Annals of Operations Research, Springer, vol. 211(1), pages 493-509, December.
  • Handle: RePEc:spr:annopr:v:211:y:2013:i:1:p:493-509:10.1007/s10479-013-1329-0
    DOI: 10.1007/s10479-013-1329-0
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    References listed on IDEAS

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    1. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
    2. Linares, Pedro, 2009. "Are inconsistent decisions better? An experiment with pairwise comparisons," European Journal of Operational Research, Elsevier, vol. 193(2), pages 492-498, March.
    3. Michele Fedrizzi & Matteo Brunelli, 2009. "Fair Consistency Evaluation For Reciprocal Relations And In Group Decision Making," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 407-420.
    4. Osei-Bryson, Kweku-Muata, 2006. "An action learning approach for assessing the consistency of pairwise comparison data," European Journal of Operational Research, Elsevier, vol. 174(1), pages 234-244, October.
    5. Stein, William E. & Mizzi, Philip J., 2007. "The harmonic consistency index for the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 177(1), pages 488-497, February.
    6. Marcin Anholcer & Volodymyr Babiy & Sándor Bozóki & Waldemar Koczkodaj, 2011. "A simplified implementation of the least squares solution for pairwise comparisons matrices," 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(4), pages 439-444, December.
    7. Salo, Ahti A. & Hamalainen, Raimo P., 1995. "Preference programming through approximate ratio comparisons," European Journal of Operational Research, Elsevier, vol. 82(3), pages 458-475, May.
    8. Saaty, Thomas L., 1994. "Highlights and critical points in the theory and application of the Analytic Hierarchy Process," European Journal of Operational Research, Elsevier, vol. 74(3), pages 426-447, May.
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