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On the Mathematical Foundation of MACBETH

In: Multiple Criteria Decision Analysis: State of the Art Surveys

Author

Listed:
  • Carlos A. Bana e Costa

    (Centre for Management Studies of Instituto Superior Técnico Technical University of Lisbon
    London School of Economics)

  • Jean-Marie Corte

    (Université de Mons-Hainaut)

  • Jean-Claude Vansnick

    (Université de Mons-Hainaut)

Abstract

MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique) is a multicriteria decision analysis approach that requires only qualitative judgements about differences of value to help an individual or a group quantify the relative attractiveness of options. This chapter presents an up-to-date survey of the mathematical foundations of MACBETH. Reference is also made to real-world applications and an extensive bibliography, spanning back to the early 1990’s, is provided.

Suggested Citation

  • Carlos A. Bana e Costa & Jean-Marie Corte & Jean-Claude Vansnick, 2005. "On the Mathematical Foundation of MACBETH," International Series in Operations Research & Management Science, in: Multiple Criteria Decision Analysis: State of the Art Surveys, chapter 0, pages 409-437, Springer.
    • Handle: RePEc:spr:isochp:978-0-387-23081-8_10
    DOI: 10.1007/0-387-23081-5_10
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    Cited by:

    1. Merad, Myriam & Dechy, Nicolas & Serir, Lisa & Grabisch, Michel & Marcel, Frédéric, 2013. "Using a multi-criteria decision aid methodology to implement sustainable development principles within an organization," European Journal of Operational Research, Elsevier, vol. 224(3), pages 603-613.
    2. de Almeida, Jonatas Araujo & Costa, Ana Paula Cabral Seixas & de Almeida-Filho, Adiel Teixeira, 2016. "A new method for elicitation of criteria weights in additive models: Flexible and interactive tradeoffAuthor-Name: de Almeida, Adiel Teixeira," European Journal of Operational Research, Elsevier, vol. 250(1), pages 179-191.
    3. F A F Ferreira & S P Santos & P M M Rodrigues, 2011. "Adding value to bank branch performance evaluation using cognitive maps and MCDA: a case study," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1320-1333, July.
    4. Dorota Górecka & Ewa Roszkowska & Tomasz Wachowicz, 2016. "The MARS Approach in the Verbal and Holistic Evaluation of the Negotiation Template," Group Decision and Negotiation, Springer, vol. 25(6), pages 1097-1136, November.
    5. Paulo H. Baumann & Tiago Milagres Miranda & Fabio Romero & Dário Takahata & Alden Uehara Antunes & João Castilho Neto & Leonardo H. T. Ferreira Neto & Ângelo C. Lorenzo Alves & Luísa Morais Azevedo & , 2016. "Crew Dispatch for Commercial and Technical Services in an Electric Power Distribution Company Using ACO Technique," Asian Engineering Review, Asian Online Journal Publishing Group, vol. 3(3), pages 17-23.
    6. Grazia Napoli & Maria Rosa Trovato & Simona Barbaro, 2022. "Social Housing and Affordable Rent: The Effectiveness of Legal Thresholds of Rents in Two Italian Metropolitan Cities," Sustainability, MDPI, vol. 14(12), pages 1-32, June.
    7. Madeira, Armando Gonçalves & Cardoso, Moacyr Machado & Belderrain, Mischel Carmen Neyra & Correia, Anderson Ribeiro & Schwanz, Silvia Helena, 2012. "Multicriteria and multivariate analysis for port performance evaluation," International Journal of Production Economics, Elsevier, vol. 140(1), pages 450-456.
    8. Gomes, Luís S. & Santos, Sérgio P. & Coelho, Luís Serra & Rebelo, Efigénio L., 2023. "Using MCDA to assist an Intermunicipal community develop a resilience strategy in face of the pandemic caused by the SARS-CoV-2," Socio-Economic Planning Sciences, Elsevier, vol. 87(PB).
    9. Adiel Teixeira Almeida & Eduarda Asfora Frej & Lucia Reis Peixoto Roselli, 2021. "Combining holistic and decomposition paradigms in preference modeling with the flexibility of FITradeoff," 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. 29(1), pages 7-47, March.
    10. Mousset, Céline, 2009. "Families of relations modelling preferences under incomplete information," European Journal of Operational Research, Elsevier, vol. 192(2), pages 538-548, January.
    11. Jairo Cugliari & Antoine Rolland, 2018. "Simulation of multicriteria data," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 6(1), pages 21-37, June.
    12. Stefan Hajkowicz & Kerry Collins, 2007. "A Review of Multiple Criteria Analysis for Water Resource Planning and Management," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 21(9), pages 1553-1566, September.
    13. Vieira, Ana C.L. & Oliveira, Mónica D. & Bana e Costa, Carlos A., 2020. "Enhancing knowledge construction processes within multicriteria decision analysis: The Collaborative Value Modelling framework," Omega, Elsevier, vol. 94(C).
    14. Figueira, José Rui & Greco, Salvatore & Slowinski, Roman, 2009. "Building a set of additive value functions representing a reference preorder and intensities of preference: GRIP method," European Journal of Operational Research, Elsevier, vol. 195(2), pages 460-486, June.
    15. Cavallaro, Fausto, 2010. "A comparative assessment of thin-film photovoltaic production processes using the ELECTRE III method," Energy Policy, Elsevier, vol. 38(1), pages 463-474, January.
    16. Johanna Vásquez & Sergio Botero, 2020. "Hybrid Methodology to Improve Health Status Utility Values Derivation Using EQ-5D-5L and Advanced Multi-Criteria Techniques," IJERPH, MDPI, vol. 17(4), pages 1-18, February.
    17. Toly Chen, 2021. "A diversified AHP-tree approach for multiple-criteria supplier selection," Computational Management Science, Springer, vol. 18(4), pages 431-453, October.
    18. L. A. Shah & A. Etienne & A. Siadat & F. Vernadat, 2016. "Decision-making in the manufacturing environment using a value-risk graph," Journal of Intelligent Manufacturing, Springer, vol. 27(3), pages 617-630, June.
    19. Bana e Costa, Carlos A. & Oliveira, Mónica D. & Rodrigues, Teresa C. & Vieira, Ana C.L., 2023. "Desirability–doability group judgment framework for the collaborative multicriteria evaluation of public policies," LSE Research Online Documents on Economics 118192, London School of Economics and Political Science, LSE Library.
    20. Kadziński, Miłosz & Greco, Salvatore & Słowiński, Roman, 2013. "RUTA: A framework for assessing and selecting additive value functions on the basis of rank related requirements," Omega, Elsevier, vol. 41(4), pages 735-751.

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