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Generalized Multiple Averaging Operators and their Applications to Group Decision Making

Author

Listed:
  • Ligang Zhou

    (Anhui University)

  • Huayou Chen

    (Anhui University)

  • Jinpei Liu

    (Tianjin University)

Abstract

In this paper, we present a new operator called the generalized ordered weighted multiple averaging (GOWMA) operator based on a minimization problem with penalty function, which unifies the geometric mean and the generalized ordered weighted averaging operator with the generalized ordered weighted harmonic averaging operator in the same formulation. We study different properties and families of the GOWMA operator and develop a generalization of this operator called the generalized hybrid multiple averaging operator. To determine the GOWMA operator weights, we propose the generalized least squares method which does not follow a regular distribution. Finally, we give a numerical example of an investment selection to illustrate the application of the GOWMA operator to multiple attribute group decision making.

Suggested Citation

  • Ligang Zhou & Huayou Chen & Jinpei Liu, 2013. "Generalized Multiple Averaging Operators and their Applications to Group Decision Making," Group Decision and Negotiation, Springer, vol. 22(2), pages 331-358, March.
    • Handle: RePEc:spr:grdene:v:22:y:2013:i:2:d:10.1007_s10726-011-9267-1
    DOI: 10.1007/s10726-011-9267-1
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    References listed on IDEAS

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    1. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2011. "Aggregation functions: Means," Post-Print hal-00539028, HAL.
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    Cited by:

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    2. Donghai Liu & Xiaohong Chen & Dan Peng, 2017. "Interval-Valued Intuitionistic Fuzzy Ordered Weighted Cosine Similarity Measure and Its Application in Investment Decision-Making," Complexity, Hindawi, vol. 2017, pages 1-11, February.
    3. Merigó, José M. & Palacios-Marqués, Daniel & del Mar Benavides-Espinosa, María, 2015. "Aggregation methods to calculate the average price," Journal of Business Research, Elsevier, vol. 68(7), pages 1574-1580.
    4. Gao, Jianwei & Li, Ming & Liu, Huihui, 2015. "Generalized ordered weighted utility proportional averaging-hyperbolic absolute risk aversion operators and their applications to group decision-making," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 114-132.
    5. Hui-Chin Tang & Shen-Tai Yang, 2018. "Optimizing Three-Dimensional Constrained Ordered Weighted Averaging Aggregation Problem with Bounded Variables," Mathematics, MDPI, vol. 6(9), pages 1-16, September.
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    7. Jianwei Gao & Huihui Liu, 2017. "Generalized Ordered Weighted Reference Dependent Utility Aggregation Operators and Their Applications to Group Decision-Making," Group Decision and Negotiation, Springer, vol. 26(6), pages 1173-1207, November.

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