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Group Decision Making with Interval-Valued Intuitionistic Multiplicative Linguistic Preference Relations

Author

Listed:
  • Jie Tang

    (Central South University)

  • Fanyong Meng

    (Central South University
    Nanjing University of Information Science and Technology)

  • Francisco Javier Cabrerizo

    (University of Granada)

  • Enrique Herrera-Viedma

    (University of Granada
    King Abdulaziz University)

Abstract

To express the asymmetrically uncertain preferred and non-preferred qualitative judgments of decision makers, this paper introduces interval-valued intuitionistic multiplicative linguistic variables (IVIMLVs). To show their application in decision making, a ranking method is first offered. Then, we introduce IVIMLVs for preference relations and propose interval-valued intuitionistic multiplicative linguistic preference relations (IVIMLPRs). To obtain the ranking reasonably, a consistency definition for IVIMLPRs is presented. A mathematical optimization model for judging the consistency of IVIMLPRs based on the new concept is constructed. To address two general cases: incompleteness and inconsistency, mathematical optimization models for ascertaining unknown values in incomplete IVIMLPRs and deriving completely consistent IVIMLPRs from inconsistent ones are built, respectively. For group decision making, a consensus index is defined to measure the consensus achieved among the decision makers’ preferences. If the consensus is not enough, a mathematical optimization model for improving the consensus level is established. Furthermore, a linear optimization model for determining the weights of the decision makers based on the consensus analysis is constructed. Finally, a group decision-making method with IVIMLPRs based on consistency and consensus analysis is offered, and its application on selecting supply chain cooperative partners is offered.

Suggested Citation

  • Jie Tang & Fanyong Meng & Francisco Javier Cabrerizo & Enrique Herrera-Viedma, 2020. "Group Decision Making with Interval-Valued Intuitionistic Multiplicative Linguistic Preference Relations," Group Decision and Negotiation, Springer, vol. 29(1), pages 169-206, February.
    • Handle: RePEc:spr:grdene:v:29:y:2020:i:1:d:10.1007_s10726-019-09646-1
    DOI: 10.1007/s10726-019-09646-1
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    References listed on IDEAS

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    1. Dong, Yucheng & Xu, Yinfeng & Li, Hongyi, 2008. "On consistency measures of linguistic preference relations," European Journal of Operational Research, Elsevier, vol. 189(2), pages 430-444, September.
    2. Fanyong Meng & Qingxian An & Xiaohong Chen, 2016. "A consistency and consensus-based method to group decision making with interval linguistic preference relations," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(11), pages 1419-1437, November.
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    4. Fanyong Meng & Xiaohong Chen, 2018. "A robust additive consistency-based method for decision making with triangular fuzzy reciprocal preference relations," Fuzzy Optimization and Decision Making, Springer, vol. 17(1), pages 49-73, March.
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    7. Wenqi Liu & Yucheng Dong & Francisco Chiclana & Francisco Javier Cabrerizo & Enrique Herrera-Viedma, 2017. "Group decision-making based on heterogeneous preference relations with self-confidence," Fuzzy Optimization and Decision Making, Springer, vol. 16(4), pages 429-447, December.
    8. Meng, Fanyong & Tan, Chunqiao & Chen, Xiaohong, 2017. "Multiplicative consistency analysis for interval fuzzy preference relations: A comparative study," Omega, Elsevier, vol. 68(C), pages 17-38.
    9. Qingxian An & Fanyong Meng & Beibei Xiong, 2018. "Interval cross efficiency for fully ranking decision making units using DEA/AHP approach," Annals of Operations Research, Springer, vol. 271(2), pages 297-317, December.
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