IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i5p813-d359407.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/5/813/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/5/813/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Michel Grabisch, 2016. "Set Functions, Games and Capacities in Decision Making," Theory and Decision Library C, Springer, number 978-3-319-30690-2, December.
    4. 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.
    5. 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.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bice Cavallo, 2019. "Coherent weights for pairwise comparison matrices and a mixed-integer linear programming problem," Journal of Global Optimization, Springer, vol. 75(1), pages 143-161, September.
    2. Fischer, Barbara & Telser, Harry & Zweifel, Peter & von Wyl, Viktor & Beck, Konstantin & Weber, Andreas, 2023. "The value of a QALY towards the end of life and its determinants: Experimental evidence," Social Science & Medicine, Elsevier, vol. 326(C).
    3. Chavez, Daniel E. & Palma, Marco A. & Nayga, Rodolfo M. & Mjelde, James W., 2020. "Product availability in discrete choice experiments with private goods," Journal of choice modelling, Elsevier, vol. 36(C).
    4. Ishizaka, Alessio & Siraj, Sajid & Nemery, Philippe, 2016. "Which energy mix for the UK (United Kingdom)? An evolutive descriptive mapping with the integrated GAIA (graphical analysis for interactive aid)–AHP (analytic hierarchy process) visualization tool," Energy, Elsevier, vol. 95(C), pages 602-611.
    5. Mahieu, Pierre-Alexandre & Andersson, Henrik & Beaumais, Olivier & Crastes dit Sourd, Romain & Hess, François-Charles & Wolff, François-Charles, 2017. "Stated preferences: a unique database composed of 1657 recent published articles in journals related to agriculture, environment, or health," Review of Agricultural, Food and Environmental Studies, Institut National de la Recherche Agronomique (INRA), vol. 98(3), November.
    6. Michel Grabisch, 2016. "Remarkable polyhedra related to set functions, games and capacities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 301-326, July.
    7. Mikhailov, L., 2004. "A fuzzy approach to deriving priorities from interval pairwise comparison judgements," European Journal of Operational Research, Elsevier, vol. 159(3), pages 687-704, December.
    8. Jennifer A Whitty & Simon Stewart & Melinda J Carrington & Alicia Calderone & Thomas Marwick & John D Horowitz & Henry Krum & Patricia M Davidson & Peter S Macdonald & Christopher Reid & Paul A Scuffh, 2013. "Patient Preferences and Willingness-To-Pay for a Home or Clinic Based Program of Chronic Heart Failure Management: Findings from the Which? Trial," PLOS ONE, Public Library of Science, vol. 8(3), pages 1-8, March.
    9. Nikita Arora & Matthew Quaife & Kara Hanson & Mylene Lagarde & Dorka Woldesenbet & Abiy Seifu & Romain Crastes dit Sourd, 2022. "Discrete choice analysis of health worker job preferences in Ethiopia: Separating attribute non‐attendance from taste heterogeneity," Health Economics, John Wiley & Sons, Ltd., vol. 31(5), pages 806-819, May.
    10. Chen, Gang & Ratcliffe, Julie & Milte, Rachel & Khadka, Jyoti & Kaambwa, Billingsley, 2021. "Quality of care experience in aged care: An Australia-Wide discrete choice experiment to elicit preference weights," Social Science & Medicine, Elsevier, vol. 289(C).
    11. Catherine L. Kling & Daniel J. Phaneuf & Jinhua Zhao, 2012. "From Exxon to BP: Has Some Number Become Better Than No Number?," Journal of Economic Perspectives, American Economic Association, vol. 26(4), pages 3-26, Fall.
    12. Michel Grabisch & Agnieszka Rusinowska, 2020. "k -additive upper approximation of TU-games," PSE-Ecole d'économie de Paris (Postprint) halshs-02860802, HAL.
    13. Yahya, Salleh & Kingsman, Brian, 2002. "Modelling a multi-objective allocation problem in a government sponsored entrepreneur development programme," European Journal of Operational Research, Elsevier, vol. 136(2), pages 430-448, January.
    14. John Buckell & Vrinda Vasavada & Sarah Wordsworth & Dean A. Regier & Matthew Quaife, 2022. "Utility maximization versus regret minimization in health choice behavior: Evidence from four datasets," Health Economics, John Wiley & Sons, Ltd., vol. 31(2), pages 363-381, February.
    15. Dunsch, Felipe Alexander & Velenyi, Edit, 2019. "Job Preferences of Frontline Health Workers in Ghana - A Discrete Choice Experiment," SocArXiv bqx5k, Center for Open Science.
    16. Ulrich Faigle & Michel Grabisch, 2019. "Least Square Approximations and Linear Values of Cooperative Game," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02381231, HAL.
    17. Lucie Lidinska & Josef Jablonsky, 2018. "AHP model for performance evaluation of employees in a Czech management consulting company," 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. 26(1), pages 239-258, March.
    18. Brouwers, Jonas & Cox, Bianca & Van Wilder, Astrid & Claessens, Fien & Bruyneel, Luk & De Ridder, Dirk & Eeckloo, Kristof & Vanhaecht, Kris, 2021. "The future of hospital quality of care policy: A multi-stakeholder discrete choice experiment in Flanders, Belgium," Health Policy, Elsevier, vol. 125(12), pages 1565-1573.
    19. Diaz, Lina & Houser, Daniel & Ifcher, John & Zarghamee, Homa, 2023. "Estimating social preferences using stated satisfaction: Novel support for inequity aversion," European Economic Review, Elsevier, vol. 155(C).
    20. Takao Asano & Hiroyuki Kojima, 2022. "Choquet Integrals and Belief Functions," KIER Working Papers 1077, Kyoto University, Institute of Economic Research.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:813-:d:359407. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.