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$$\mathcal {G}$$ G -distance and $$\mathcal {G}$$ G -decomposition for improving $$\mathcal {G}$$ G -consistency of a Pairwise Comparison Matrix

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  • Bice Cavallo

    (University of Naples “Federico II”)

Abstract

Pairwise comparisons have been a long standing technique for comparing alternatives/criteria and their role has been pivotal in the development of modern decision making methods. Since consistency ensures rational decisions, in literature several approaches are proposed for the revision of the Pairwise Comparison Matrix in order to improve its consistency. In order to obtain general results, suitable for several kinds of Pairwise Comparison Matrices proposed in literature, we focus on matrices defined over a general unifying framework, that is an Abelian linearly ordered group. In this context, firstly, we provide $$\mathcal {G}$$ G -distance between Pairwise Comparison Matrices and $$\mathcal {G}$$ G -decomposition of a Pairwise Comparison Matrix in its $$\mathcal {G}$$ G -consistent and totally $$\mathcal {G}$$ G -inconsistent components. Then, we show how a $$\mathcal {G}$$ G -inconsistent Pairwise Comparison Matrix can be revised according to the associated $$\mathcal {G}$$ G -consistent component; the revision process takes into account $$\mathcal {G}$$ G -distance from the former in order to better represent decision maker’s preferences.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:fuzodm:v:18:y:2019:i:1:d:10.1007_s10700-018-9286-3
    DOI: 10.1007/s10700-018-9286-3
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    References listed on IDEAS

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    1. 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.
    2. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
    3. Wenqi Liu & Yucheng Dong & Francisco Chiclana & Francisco Javier Cabrerizo & Enrique Herrera-Viedma, 2017. "Group decision-making based on heterogeneous preference relations with self-confidence," Fuzzy Optimization and Decision Making, Springer, vol. 16(4), pages 429-447, December.
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