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A general formulation for some inconsistency indices of pairwise comparisons

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  • Matteo Brunelli

    (University of Trento)

  • Michele Fedrizzi

    (University of Trento)

Abstract

We propose a unifying approach to the problem of measuring the inconsistency of judgments. More precisely, we define a general framework to allow several well-known inconsistency indices to be expressed as special cases of this new formulation. We consider inconsistency indices as aggregations of ‘local’, i.e. triple-based, inconsistencies. We show that few reasonable assumptions guarantee a set of good properties for the obtained general inconsistency index. Under this representation, we prove a property of Pareto efficiency and show that OWA functions and t-conorms are suitable aggregation functions of local inconsistencies. We argue that the flexibility of this proposal allows tuning of the index. For example, by using different types of OWA functions, the analyst can obtain the desired balance between an averaging behavior and a ‘largest inconsistency-focused’ behavior.

Suggested Citation

  • Matteo Brunelli & Michele Fedrizzi, 2019. "A general formulation for some inconsistency indices of pairwise comparisons," Annals of Operations Research, Springer, vol. 274(1), pages 155-169, March.
    • Handle: RePEc:spr:annopr:v:274:y:2019:i:1:d:10.1007_s10479-018-2936-6
    DOI: 10.1007/s10479-018-2936-6
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    References listed on IDEAS

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    1. Matteo Brunelli & Michele Fedrizzi, 2015. "Axiomatic properties of inconsistency indices for pairwise comparisons," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(1), pages 1-15, January.
    2. 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.
    3. Paul Thaddeus Kazibudzki, 2016. "An examination of performance relations among selected consistency measures for simulated pairwise judgments," Annals of Operations Research, Springer, vol. 244(2), pages 525-544, September.
    4. Can, Burak, 2014. "Weighted distances between preferences," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 109-115.
    5. Juan Aguarón & María Teresa Escobar & José María Moreno-Jiménez, 2016. "The precise consistency consensus matrix in a local AHP-group decision making context," Annals of Operations Research, Springer, vol. 245(1), pages 245-259, October.
    6. Carmone, Frank J. & Kara, Ali & Zanakis, Stelios H., 1997. "A Monte Carlo investigation of incomplete pairwise comparison matrices in AHP," European Journal of Operational Research, Elsevier, vol. 102(3), pages 538-553, November.
    7. József Temesi, 2011. "Pairwise comparison matrices and the error-free property of the decision maker," 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 239-249, June.
    8. Pajala, Tommi & Korhonen, Pekka & Wallenius, Jyrki, 2017. "Road to robust prediction of choices in deterministic MCDM," European Journal of Operational Research, Elsevier, vol. 259(1), pages 229-235.
    9. Waldemar W. Koczkodaj & Konrad Kułakowski & Antoni Ligęza, 2014. "On the quality evaluation of scientific entities in Poland supported by consistency-driven pairwise comparisons method," Scientometrics, Springer;Akadémiai Kiadó, vol. 99(3), pages 911-926, June.
    10. Siraj, Sajid & Mikhailov, Ludmil & Keane, John A., 2015. "Contribution of individual judgments toward inconsistency in pairwise comparisons," European Journal of Operational Research, Elsevier, vol. 242(2), pages 557-567.
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    Cited by:

    1. Csató, László & Petróczy, Dóra Gréta, 2021. "On the monotonicity of the eigenvector method," European Journal of Operational Research, Elsevier, vol. 292(1), pages 230-237.
    2. Michele Fedrizzi & Nino Civolani & Andrew Critch, 2020. "Inconsistency evaluation in pairwise comparison using norm-based distances," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 657-672, December.
    3. László Csató, 2019. "Axiomatizations of inconsistency indices for triads," Annals of Operations Research, Springer, vol. 280(1), pages 99-110, September.

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