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A robust additive consistency-based method for decision making with triangular fuzzy reciprocal preference relations

Author

Listed:
  • Fanyong Meng

    (Nanjing Audit University
    Central South University)

  • Xiaohong Chen

    (Central South University
    Hunan University of Commerce)

Abstract

To express uncertain information in decision making, triangular fuzzy reciprocal preference relations (TFRPRs) might be adopted by decision makers. Considering consistency of this type of preference relations, this paper defines a new additive consistency concept, which can be seen as an extension of that for reciprocal preference relations. Then, a simple method to calculate the triangular fuzzy priority weight vector is introduced. When TFRPRs are inconsistent, a linear goal programming framework to derive the completely additive consistent TFRPRs is provided. Meanwhile, an improved linear goal programming model is constructed to estimate the missing values in an incomplete TFRPR that can address the situation where ignored objects exist. After that, an algorithm for decision making with TFRPRs is presented. Finally, numerical examples and comparison analysis are offered.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:fuzodm:v:17:y:2018:i:1:d:10.1007_s10700-016-9262-8
    DOI: 10.1007/s10700-016-9262-8
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    References listed on IDEAS

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    1. Saaty, Thomas L. & Vargas, Luis G., 1987. "Uncertainty and rank order in the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 32(1), pages 107-117, October.
    2. Leung, L. C. & Cao, D., 2000. "On consistency and ranking of alternatives in fuzzy AHP," European Journal of Operational Research, Elsevier, vol. 124(1), pages 102-113, July.
    3. Liu, Fang & Zhang, Wei-Guo & Zhang, Li-Hua, 2014. "Consistency analysis of triangular fuzzy reciprocal preference relations," European Journal of Operational Research, Elsevier, vol. 235(3), pages 718-726.
    4. Chang, Da-Yong, 1996. "Applications of the extent analysis method on fuzzy AHP," European Journal of Operational Research, Elsevier, vol. 95(3), pages 649-655, December.
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    Cited by:

    1. Hongyue Diao & Ansheng Deng & Hui Cui & Xin Liu & Li Zou, 2022. "An approach for solving fuzzy multi-criteria decision problem under linguistic information," Fuzzy Optimization and Decision Making, Springer, vol. 21(1), pages 45-69, March.
    2. 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.
    3. Zhibin Wu & Rong Yuan & Jiancheng Tu, 2021. "Group Decision Making with Transitive Preferences Under Ordinal and Cardinal Consistencies: An Optimization Approach," Group Decision and Negotiation, Springer, vol. 30(1), pages 221-250, February.
    4. 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.

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