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

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  • Pelegrina, Guilherme Dean
  • Duarte, Leonardo Tomazeli
  • Grabisch, Michel
  • Romano, João Marcos Travassos

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

  • Pelegrina, Guilherme Dean & Duarte, Leonardo Tomazeli & Grabisch, Michel & Romano, João Marcos Travassos, 2020. "The multilinear model in multicriteria decision making: The case of 2-additive capacities and contributions to parameter identification," European Journal of Operational Research, Elsevier, vol. 282(3), pages 945-956.
    • Handle: RePEc:eee:ejores:v:282:y:2020:i:3:p:945-956
    DOI: 10.1016/j.ejor.2019.10.005
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    Cited by:

    1. 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.
    2. Khaled Belahcène & Vincent Mousseau & Wassila Ouerdane & Marc Pirlot & Olivier Sobrie, 2024. "A guided tour of multiple criteria sorting models and methods," Annals of Operations Research, Springer, vol. 343(2), pages 785-845, December.
    3. 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.
    4. 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.
    5. 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).
    6. 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).

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