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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. Can, Burak, 2014. "Weighted distances between preferences," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 109-115.
    2. 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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    8. 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.
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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. László Csató, 2019. "Axiomatizations of inconsistency indices for triads," Annals of Operations Research, Springer, vol. 280(1), pages 99-110, September.
    3. 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.

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