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Incoherence measures and relations between coherence conditions for pairwise comparisons

Author

Listed:
  • Matteo Brunelli

    (University of Trento)

  • Bice Cavallo

    (University of Naples Federico II)

Abstract

Coherence of preferences, and the measurement of its violation, has been a long-standing issue in decision analysis. This paper continues the inquiry into coherence conditions for pairwise comparisons following a distance-based approach, in which the deviations from coherence conditions are measured on a continuous scale. Firstly, we consider eight coherence conditions already introduced in the literature and provide a complete study on their inclusion relations. Then, we consider four of these conditions and introduce optimization problems to quantify the extent of their violation.

Suggested Citation

  • Matteo Brunelli & Bice Cavallo, 2020. "Incoherence measures and relations between coherence conditions for pairwise comparisons," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 613-635, December.
    • Handle: RePEc:spr:decfin:v:43:y:2020:i:2:d:10.1007_s10203-020-00291-x
    DOI: 10.1007/s10203-020-00291-x
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    References listed on IDEAS

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    1. Thomas Saaty & Luis Vargas, 2012. "The possibility of group choice: pairwise comparisons and merging functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 481-496, March.
    2. Angilella, Silvia & Mazzù, Sebastiano, 2015. "The financing of innovative SMEs: A multicriteria credit rating model," European Journal of Operational Research, Elsevier, vol. 244(2), pages 540-554.
    3. Irving H. Lavalle & Peter C. Fishburn, 1987. "Decision Analysis Under States-Additive SSB Preferences," Operations Research, INFORMS, vol. 35(5), pages 722-735, October.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Bice Cavallo & Alessio Ishizaka, 2023. "Evaluating scales for pairwise comparisons," Annals of Operations Research, Springer, vol. 325(2), pages 951-965, June.
    2. Matteo Brunelli & Michele Fedrizzi & Salvatore Greco & José Rui Figueira & Roman Słowiński, 2020. "A special issue on multi-criteria decision aiding," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 557-558, December.
    3. 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.

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    More about this item

    Keywords

    Pairwise comparisons; Preference relations; Coherence; Mixed-integer linear programming;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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