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A consistency and consensus-based method to group decision making with interval linguistic preference relations

Author

Listed:
  • Fanyong Meng

    (Central South University)

  • Qingxian An

    (Central South University)

  • Xiaohong Chen

    (Central South University
    Hunan University of Commerce)

Abstract

Preference relations are a powerful tool to address decision-making problems. In some situations, because of the complexity of decision-making problems and the inherent uncertainty, the decision makers cannot express their preferences by using numerical values. Interval linguistic preference relations, which are more reliable and informative for the decision-makers’ preferences, are a good choice to cope with this issue. Just as with the other types of preference relations, the consistency and consensus analysis is very importance to ensure the reasonable ranking order by using interval linguistic preference relations. Considering this situation, this paper introduces a consistency concept for interval linguistic preference relations. To measure the consistency of interval linguistic preference relations, a consistency measure is defined. Then, a consistency-based programming model is built, by which the consistent linguistic preference relations with respect to each object can be obtained. To cope with the inconsistency case, two models for deriving the adjusted consistent linguistic preference relations are constructed. Then, a consistency-based programming model to estimate the missing values is built. After that, we present a group consensus index and present some of its desirable properties. Furthermore, a group consensus-based model to determine the weights of the decision makers with respect to each object is established. Finally, an approach to group decision making with interval linguistic preference relations is developed, which is based on the consistency and consensus analysis. Meanwhile, the associated numerical examples are offered to illustrate the application of the procedure.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:jorsoc:v:67:y:2016:i:11:d:10.1057_jors.2016.28
    DOI: 10.1057/jors.2016.28
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    References listed on IDEAS

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    1. Dong, Yucheng & Xu, Yinfeng & Li, Hongyi & Feng, Bo, 2010. "The OWA-based consensus operator under linguistic representation models using position indexes," European Journal of Operational Research, Elsevier, vol. 203(2), pages 455-463, June.
    2. 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.
    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. Herrera, F. & Herrera-Viedma, E., 2000. "Choice functions and mechanisms for linguistic preference relations," European Journal of Operational Research, Elsevier, vol. 120(1), pages 144-161, January.
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    Cited by:

    1. Yong Liu & Ting Zhou & Wei-xue Diao & Jinhong Yi, 2022. "A multivariate minimum cost consensus approach for two-level group decision making," OPSEARCH, Springer;Operational Research Society of India, vol. 59(3), pages 839-861, September.
    2. Wenqi Liu & Hengjie Zhang & Haiming Liang & Cong-cong Li & Yucheng Dong, 2022. "Managing Consistency and Consensus Issues in Group Decision-Making with Self-Confident Additive Preference Relations and Without Feedback: A Nonlinear Optimization Method," Group Decision and Negotiation, Springer, vol. 31(1), pages 213-240, February.
    3. 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.
    4. Jie Tang & Qingxian An & Fanyong Meng & Xiaohong Chen, 2017. "A Natural Method for Ranking Objects from Hesitant Fuzzy Preference Relations," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(06), pages 1611-1646, November.
    5. Sha Fan & Hengjie Zhang & Huali Tang, 2019. "A Linguistic Hierarchy Model with Self-Confidence Preference Relations and Its Application in Co-Regulation of Food Safety in China," IJERPH, MDPI, vol. 16(16), pages 1-21, August.
    6. Pei Wang & Xuanhua Xu & Shuai Huang, 2019. "An Improved Consensus-Based Model for Large Group Decision Making Problems Considering Experts with Linguistic Weighted Information," Group Decision and Negotiation, Springer, vol. 28(3), pages 619-640, June.
    7. Zhang, Hengjie & Dong, Yucheng & Chiclana, Francisco & Yu, Shui, 2019. "Consensus efficiency in group decision making: A comprehensive comparative study and its optimal design," European Journal of Operational Research, Elsevier, vol. 275(2), pages 580-598.
    8. 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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