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Nonadditivity Index Based Quasi-Random Generation of Capacities and Its Application in Comprehensive Decision Aiding

Author

Listed:
  • Li Huang

    (School of Business, Ningbo University, Ningbo 315211, China)

  • Jian-Zhang Wu

    (School of Business, Ningbo University, Ningbo 315211, China)

  • Rui-Jie Xi

    (School of Business, Ningbo University, Ningbo 315211, China)

Abstract

The capacity is a powerful tool with exponential coefficients to represent the interaction phenomenon among decision criteria, but its random generation becomes a tough issue for dealing with the monotonicity with all inclusion subsets as well as the complex constraints of decision preference. In this paper, we adopt a kind of explicit interaction index, the nonadditivity index, to construct two types of quasi-random generation methods of capacity under a given decision interaction preference. Compared to the existing random generation algorithms, the methods have relatively satisfactory performance on the statistics characteristic of generated capacities but need rather less calculation effort on the generation process. We also show the effectiveness of proposed quasi-random generation methods by an illustrative decision example.

Suggested Citation

  • Li Huang & Jian-Zhang Wu & Rui-Jie Xi, 2020. "Nonadditivity Index Based Quasi-Random Generation of Capacities and Its Application in Comprehensive Decision Aiding," Mathematics, MDPI, vol. 8(2), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:301-:d:324523
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    References listed on IDEAS

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    1. Michel Grabisch, 2016. "Set Functions, Games and Capacities in Decision Making," Theory and Decision Library C, Springer, number 978-3-319-30690-2, September.
    2. 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.
    3. Michel Grabisch & Christophe Labreuche, 2010. "A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid," Annals of Operations Research, Springer, vol. 175(1), pages 247-286, March.
    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.
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