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The multilinear model in multicriteria decision making: The case of 2-additive capacities and contributions to parameter identification

Author

Listed:
  • Guilherme Dean Pelegrina

    (DSPCom - Laboratory of Signal Processing for Communications - UNICAMP - Universidade Estadual de Campinas = University of Campinas, UNICAMP - Universidade Estadual de Campinas = University of Campinas, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Leonardo Tomazeli Duarte

    (UNICAMP - Universidade Estadual de Campinas = University of Campinas)

  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • João Marcos Travassos Romano

    (UnB - University of Brasilia [Brazil])

Abstract
In several multicriteria decision making problems, it is important to consider interactions among criteria in order to satisfy the preference relations provided by the decision maker. This can be achieved by using aggregation functions based on fuzzy measures, such as the Choquet integral and the multilinear model. Although the Choquet integral has been studied in a large number of works, one does not find the same literature with respect to the multilinear model. In this context, the contribution of this work is twofold. We first provide a formulation of the multilinear model by means of a 2-additive capacity. A second contribution lies in the problem of capacity identification. We consider a supervised approach and apply optimization models with and without regularization terms. Results obtained in numerical experiments with both synthetic and real data attest the performance of the considered approaches.

Suggested Citation

  • Guilherme Dean Pelegrina & Leonardo Tomazeli Duarte & Michel Grabisch & João Marcos Travassos Romano, 2020. "The multilinear model in multicriteria decision making: The case of 2-additive capacities and contributions to parameter identification," PSE-Ecole d'économie de Paris (Postprint) halshs-02379646, HAL.
    • Handle: RePEc:hal:pseptp:halshs-02379646
    DOI: 10.1016/j.ejor.2019.10.005
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-02379646
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    References listed on IDEAS

    as
    1. Marichal, Jean-Luc & Roubens, Marc, 2000. "Determination of weights of interacting criteria from a reference set," European Journal of Operational Research, Elsevier, vol. 124(3), pages 641-650, August.
    2. Kolesárová, Anna & Li, Jun & Mesiar, Radko, 2018. "k-additive aggregation functions and their characterization," European Journal of Operational Research, Elsevier, vol. 265(3), pages 985-992.
    3. Michel Grabisch & Guilherme Dean Pelegrina & Leonardo Tomazeli Duarte & Joao Marcos T. Romano, 2018. "Multilinear model: New issues in capacity identification," Post-Print halshs-03221043, HAL.
    4. Grabisch, Michel & Kojadinovic, Ivan & Meyer, Patrick, 2008. "A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package," European Journal of Operational Research, Elsevier, vol. 186(2), pages 766-785, April.
    5. Michel Grabisch & Jean-Luc Marichal & Marc Roubens, 2000. "Equivalent Representations of Set Functions," Mathematics of Operations Research, INFORMS, vol. 25(2), pages 157-178, May.
    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. Kojadinovic, Ivan, 2004. "Estimation of the weights of interacting criteria from the set of profiles by means of information-theoretic functionals," European Journal of Operational Research, Elsevier, vol. 155(3), pages 741-751, June.
    8. Li, Gang & Law, Rob & Vu, Huy Quan & Rong, Jia, 2013. "Discovering the hotel selection preferences of Hong Kong inbound travelers using the Choquet Integral," Tourism Management, Elsevier, vol. 36(C), pages 321-330.
    9. repec:hal:pseose:hal-01372858 is not listed on IDEAS
    10. Michel Grabisch & Christophe Labreuche, 2016. "Fuzzy Measures and Integrals in MCDA," International Series in Operations Research & Management Science, in: Salvatore Greco & Matthias Ehrgott & José Rui Figueira (ed.), Multiple Criteria Decision Analysis, edition 2, chapter 0, pages 553-603, Springer.
    11. Denis Bouyssou & Marc Pirlot, 2004. "Preferences for multi-attributed alternatives: Traces, Dominance, and Numerical Representations," Post-Print hal-00004104, HAL.
    12. Michel Grabisch, 2016. "Set Functions, Games and Capacities in Decision Making," Theory and Decision Library C, Springer, number 978-3-319-30690-2, December.
    13. Angilella, Silvia & Corrente, Salvatore & Greco, Salvatore, 2015. "Stochastic multiobjective acceptability analysis for the Choquet integral preference model and the scale construction problem," European Journal of Operational Research, Elsevier, vol. 240(1), pages 172-182.
    14. Denis Bouyssou & Marc Pirlot, 2004. "Preferences for multi-attributed alternatives: Traces, Dominance, and Numerical Representations," Post-Print hal-00004104, HAL.
    15. Bottero, M. & Ferretti, V. & Figueira, J.R. & Greco, S. & Roy, B., 2018. "On the Choquet multiple criteria preference aggregation model: Theoretical and practical insights from a real-world application," European Journal of Operational Research, Elsevier, vol. 271(1), pages 120-140.
    16. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
    17. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 2004. "Axiomatic characterization of a general utility function and its particular cases in terms of conjoint measurement and rough-set decision rules," European Journal of Operational Research, Elsevier, vol. 158(2), pages 271-292, October.
    18. Angilella, Silvia & Greco, Salvatore & Matarazzo, Benedetto, 2010. "Non-additive robust ordinal regression: A multiple criteria decision model based on the Choquet integral," European Journal of Operational Research, Elsevier, vol. 201(1), pages 277-288, February.
    19. Grabisch, Michel, 1996. "The application of fuzzy integrals in multicriteria decision making," European Journal of Operational Research, Elsevier, vol. 89(3), pages 445-456, March.
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    Cited by:

    1. Beliakov, Gleb, 2022. "Knapsack problems with dependencies through non-additive measures and Choquet integral," European Journal of Operational Research, Elsevier, vol. 301(1), pages 277-286.
    2. Bilbao-Terol, Amelia & Bilbao-Terol, Celia, 2024. "The Choquet integral supported by a hedonic approach for modelling preferences in hotel selection," Omega, Elsevier, vol. 122(C).
    3. Zhang, Xinwei & Yan, Yong & Wang, Lilin & Wang, Yang, 2024. "A ranking approach for robust portfolio decision analysis based on multilinear portfolio utility functions and incomplete preference information," Omega, Elsevier, vol. 122(C).
    4. Khaled Belahcène & Vincent Mousseau & Wassila Ouerdane & Marc Pirlot & Olivier Sobrie, 2023. "Multiple criteria sorting models and methods—Part I: survey of the literature," 4OR, Springer, vol. 21(1), pages 1-46, March.
    5. Siskos, Eleftherios & Burgherr, Peter, 2022. "Multicriteria decision support for the evaluation of electricity supply resilience: Exploration of interacting criteria," European Journal of Operational Research, Elsevier, vol. 298(2), pages 611-626.

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    Keywords

    2-additive capacity; capacity identification; multilinear model; multi-attribute utility theory; multiple criteria analysis;
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