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AHP-Like Matrices and Structures—Absolute and Relative Preferences

Author

Listed:
  • David Koloseni

    (Department of Mathematics, University of Dar es Salaam, Dar es Salaam 35065, Tanzania)

  • Tove Helldin

    (School of Informatics, University of Skövde, 54128 Skövde, Sweden)

  • Vicenç Torra

    (School of Informatics, University of Skövde, 54128 Skövde, Sweden
    Hamilton Institute, Maynooth University, W23 A5Y6 Maynooth, Ireland)

Abstract

Aggregation functions are extensively used in decision making processes to combine available information. Arithmetic mean and weighted mean are some of the most used ones. In order to use a weighted mean, we need to define its weights. The Analytical Hierarchy Process (AHP) is a well known technique used to obtain weights based on interviews with experts. From the interviews we define a matrix of pairwise comparisons of the importance of the weights. We call these AHP-like matrices absolute preferences of weights. We propose another type of matrix that we call a relative preference matrix. We define this matrix with the same goal—to find the weights for weighted aggregators. We discuss how it can be used for eliciting the weights for the weighted mean and define a similar approach for the Choquet integral.

Suggested Citation

  • David Koloseni & Tove Helldin & Vicenç Torra, 2020. "AHP-Like Matrices and Structures—Absolute and Relative Preferences," Mathematics, MDPI, vol. 8(5), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:813-:d:359407
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    References listed on IDEAS

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    1. Esther W. de Bekker‐Grob & Mandy Ryan & Karen Gerard, 2012. "Discrete choice experiments in health economics: a review of the literature," Health Economics, John Wiley & Sons, Ltd., vol. 21(2), pages 145-172, February.
    2. Michel Grabisch, 2016. "Set Functions, Games and Capacities in Decision Making," Theory and Decision Library C, Springer, number 978-3-319-30690-2, March.
    3. Daniel Abril & Guillermo Navarro-Arribas & Vicenç Torra, 2012. "Choquet integral for record linkage," Annals of Operations Research, Springer, vol. 195(1), pages 97-110, May.
    4. Golany, B. & Kress, M., 1993. "A multicriteria evaluation of methods for obtaining weights from ratio-scale matrices," European Journal of Operational Research, Elsevier, vol. 69(2), pages 210-220, September.
    5. Alessio Ishizaka & Markus Lusti, 2006. "How to derive priorities in AHP: a comparative study," 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. 14(4), pages 387-400, December.
    6. Axel C. Mühlbacher & Anika Kaczynski & Peter Zweifel & F. Reed Johnson, 2016. "Experimental measurement of preferences in health and healthcare using best-worst scaling: an overview," Health Economics Review, Springer, vol. 6(1), pages 1-14, December.
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