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Group decision making based on DEA cross-efficiency with intuitionistic fuzzy preference relations

Author

Listed:
  • Jinpei Liu

    (Anhui University
    North Carolina State University)

  • Jingmiao Song

    (Anhui University)

  • Qin Xu

    (Anhui University)

  • Zhifu Tao

    (Anhui University)

  • Huayou Chen

    (Anhui University)

Abstract

The aim of this paper is to investigate a novel approach to group decision making based on DEA cross-efficiency with intuitionistic fuzzy preference relations, which can avoid information distortion and obtain more credible decision making results. An interval transform function is defined, which can transform an intuitionistic fuzzy preference relation into an interval multiplicative preference relation. Then, an interval transform function based data envelopment analysis model is developed to obtain the ranking vector of consistent intuitionistic fuzzy preference relation, in which each of the alternatives is viewed as a decision making unit. Moreover, for any intuitionistic fuzzy preference relations, we propose two DEA cross-efficiency models to get the cross-efficiency values of all alternatives, and we can calculate the normalized intuitionistic fuzzy priority weight vector of the intuitionistic fuzzy preference relation based on the cross-efficiency values. A goal programming model is investigated to derive the weight vector of decision makers. A step-by-step procedure for group decision making approach based on DEA cross-efficiency with intuitionistic fuzzy preference relations is presented. Finally, numerical examples are given to illustrate the validity and applicability of the proposed method. This is the first attempt of employing the DEA cross-efficiency to the group decision making with intuitionistic fuzzy preference relations.

Suggested Citation

  • Jinpei Liu & Jingmiao Song & Qin Xu & Zhifu Tao & Huayou Chen, 2019. "Group decision making based on DEA cross-efficiency with intuitionistic fuzzy preference relations," Fuzzy Optimization and Decision Making, Springer, vol. 18(3), pages 345-370, September.
    • Handle: RePEc:spr:fuzodm:v:18:y:2019:i:3:d:10.1007_s10700-018-9297-0
    DOI: 10.1007/s10700-018-9297-0
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    References listed on IDEAS

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    1. Zeshui Xu & Xiaoqiang Cai, 2015. "Group Decision Making with Incomplete Interval-Valued Intuitionistic Preference Relations," Group Decision and Negotiation, Springer, vol. 24(2), pages 193-215, March.
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    4. Herrera-Viedma, E. & Herrera, F. & Chiclana, F. & Luque, M., 2004. "Some issues on consistency of fuzzy preference relations," European Journal of Operational Research, Elsevier, vol. 154(1), pages 98-109, April.
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    6. Meimei Xia & Jian Chen, 2015. "Studies on Interval Multiplicative Preference Relations and Their Application to Group Decision Making," Group Decision and Negotiation, Springer, vol. 24(1), pages 115-144, January.
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    9. Liang Liang & Jie Wu & Wade D. Cook & Joe Zhu, 2008. "The DEA Game Cross-Efficiency Model and Its Nash Equilibrium," Operations Research, INFORMS, vol. 56(5), pages 1278-1288, October.
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    Cited by:

    1. Kao, Chiang & Liu, Shiang-Tai, 2022. "Group decision making in data envelopment analysis: A robot selection application," European Journal of Operational Research, Elsevier, vol. 297(2), pages 592-599.
    2. Xunjie Gou & Zeshui Xu & Xinxin Wang & Huchang Liao, 2021. "Managing consensus reaching process with self-confident double hierarchy linguistic preference relations in group decision making," Fuzzy Optimization and Decision Making, Springer, vol. 20(1), pages 51-79, March.
    3. Jinpei Liu & Zijie Qiang & Peng Wu & Pengcheng Du, 2023. "Multiple stage optimization driven group decision making method with interval linguistic fuzzy preference relations based on ordinal consistency and DEA cross-efficiency," Fuzzy Optimization and Decision Making, Springer, vol. 22(2), pages 309-336, June.

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