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A procedure for group decision making with interval-valued intuitionistic linguistic fuzzy 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 uncertain preferred and non-preferred qualitative judgments of decision makers, interval-valued intuitionistic linguistic fuzzy sets (IVILFSs) are proposed in a similar way as Atanassov and Gargov’s interval-valued intuitionistic fuzzy sets. Considering the application of IVILFSs, the concept of interval-valued intuitionistic linguistic fuzzy variables (IVILFVs) is defined and a ranking order is offered. Then, we introduce interval-valued intuitionistic linguistic fuzzy preference relations (IVILFPRs) whose elements are IVILFVs. Furthermore, an additive consistency concept is presented and a model for judging the consistency of IVILFPRs is built. Meanwhile, optimization models for deriving additively consistent IVILFPRs and for determining missing linguistic variables in incomplete IVILFPRs are constructed, respectively. For group decision making, optimization models for determining the weights of the decision makers and for improving the consensus level are established, respectively. A procedure for group decision making with IVILFPRs is developed that can cope with inconsistent and incomplete IVILFPRs. Finally, a practical group decision-making problem about evaluating express companies is selected to show the application of the new results.

Suggested Citation

  • Jie Tang & Fanyong Meng & Francisco Javier Cabrerizo & Enrique Herrera-Viedma, 2019. "A procedure for group decision making with interval-valued intuitionistic linguistic fuzzy preference relations," Fuzzy Optimization and Decision Making, Springer, vol. 18(4), pages 493-527, December.
    • Handle: RePEc:spr:fuzodm:v:18:y:2019:i:4:d:10.1007_s10700-019-09304-w
    DOI: 10.1007/s10700-019-09304-w
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    References listed on IDEAS

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    1. J. M. Tapia García & M. J. Del Moral & M. A. Martínez & E. Herrera-Viedma, 2012. "A Consensus Model For Group Decision-Making Problems With Interval Fuzzy Preference Relations," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 11(04), pages 709-725.
    2. Raman Kumar Goyal & Sakshi Kaushal, 2018. "Deriving crisp and consistent priorities for fuzzy AHP-based multicriteria systems using non-linear constrained optimization," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 195-209, June.
    3. 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.
    4. Gleb Beliakov & Simon James & Tim Wilkin, 2017. "Aggregation and consensus for preference relations based on fuzzy partial orders," Fuzzy Optimization and Decision Making, Springer, vol. 16(4), pages 409-428, December.
    5. 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.
    6. Fanyong Meng, 2018. "An approach to decision-making with triangular fuzzy reciprocal preference relations and its application," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(3), pages 567-581, February.
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