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Multicriteria Correlation Preference Information (MCCPI)-Based Ordinary Capacity Identification Method

Author

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  • Jian-Zhang Wu

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

  • Yi-Ping Zhou

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

  • Li Huang

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

  • Jun-Jie Dong

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

Abstract

Multicriteria correlation preference information (MCCPI) refers to a special type of 2-dimensional explicit information: the importance and interaction preferences regarding multiple dependent decision criteria. A few identification models have been established and implemented to transform the MCCPI into the most satisfactory 2-additive capacity. However, as one of the most commonly accepted particular type of capacity, 2-additive capacity only takes into account 2-order interactions and ignores the higher order interactions, which is not always reasonable in a real decision-making environment. In this paper, we generalize those identification models into ordinary capacity cases to freely represent the complicated situations of higher order interactions among multiple decision criteria. Furthermore, a MCCPI-based comprehensive decision aid algorithm is proposed to represent various kinds of dominance relationships of all decision alternatives as well as other useful decision aiding information. An illustrative example is adopted to show the proposed MCCPI-based capacity identification method and decision aid algorithm.

Suggested Citation

  • Jian-Zhang Wu & Yi-Ping Zhou & Li Huang & Jun-Jie Dong, 2019. "Multicriteria Correlation Preference Information (MCCPI)-Based Ordinary Capacity Identification Method," Mathematics, MDPI, vol. 7(3), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:300-:d:216813
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    References listed on IDEAS

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    1. Corrente, Salvatore & Greco, Salvatore & Ishizaka, Alessio, 2016. "Combining analytical hierarchy process and Choquet integral within non-additive robust ordinal regression," Omega, Elsevier, vol. 61(C), pages 2-18.
    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. 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.
    4. JosÉ Figueira & Salvatore Greco & Matthias Ehrogott, 2005. "Multiple Criteria Decision Analysis: State of the Art Surveys," International Series in Operations Research and Management Science, Springer, number 978-0-387-23081-8, September.
    5. 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.
    6. Chateauneuf, Alain & Jaffray, Jean-Yves, 1989. "Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 263-283, June.
    7. Marichal, Jean-Luc, 2007. "k-intolerant capacities and Choquet integrals," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1453-1468, March.
    8. Marichal, Jean-Luc, 2002. "Entropy of discrete Choquet capacities," European Journal of Operational Research, Elsevier, vol. 137(3), pages 612-624, March.
    9. 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.
    10. Thomas L. Saaty, 2013. "The Modern Science of Multicriteria Decision Making and Its Practical Applications: The AHP/ANP Approach," Operations Research, INFORMS, vol. 61(5), pages 1101-1118, October.
    11. Pedro Miranda & Michel Grabisch & Pedro Gil, 2002. "p-symmetric fuzzy measures," Post-Print hal-00273960, HAL.
    12. Patrick Meyer & Marc Roubens, 2005. "Choice, Ranking and Sorting in Fuzzy Multiple Criteria Decision Aid," International Series in Operations Research & Management Science, in: Multiple Criteria Decision Analysis: State of the Art Surveys, chapter 0, pages 471-503, Springer.
    13. Silvia Angilella & Marta Bottero & Salvatore Corrente & Valentina Ferretti & Salvatore Greco & Isabella M. Lami, 2016. "Non Additive Robust Ordinal Regression for urban and territorial planning: an application for siting an urban waste landfill," Annals of Operations Research, Springer, vol. 245(1), pages 427-456, October.
    14. 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.
    15. Kojadinovic, Ivan, 2007. "Minimum variance capacity identification," European Journal of Operational Research, Elsevier, vol. 177(1), pages 498-514, February.
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    Cited by:

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    2. Jian-Zhang Wu & Feng-Feng Chen & Yan-Qing Li & Li Huang, 2020. "Capacity Random Forest for Correlative Multiple Criteria Decision Pattern Learning," Mathematics, MDPI, vol. 8(8), pages 1-15, August.

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