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Iterative algorithms for improving consistency of intuitionistic preference relations

Author

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  • Z Xu

    (PLA University of Science and Technology, Nanjing, China)

  • M Xia

    (Tsinghua University, Beijing, China)

Abstract

Consistency of preference relations is an important research topic in decision making with preference information. The existing research about consistency mainly focuses on multiplicative preference relations, fuzzy preference relations and linguistic preference relations. Intuitionistic preference relations, each of their elements is composed of a membership degree, a non-membership degree and a hesitation degree, can better reflect the very imprecision of preferences of decision makers. There has been little research on consistency of intuitionistic preference relations up to now, and thus, it is necessary to pay attention to this issue. In this paper, we first propose an approach to constructing the consistent (or approximate consistent) intuitionistic preference relation from any intuitionistic preference relation. Then we develop a convergent iterative algorithm to improve the consistency of an intuitionistic preference relation. Moreover, we investigate the consistency of intuitionistic preference relations in group decision making situations, and show that if all individual intuitionistic preference relations are consistent, then the collective intuitionistic preference relation is also consistent. Moreover, we develop a convergent iterative algorithm to improve the consistency of all individual intuitionistic preference relations. The practicability and effectiveness of the developed algorithms is verified through two examples.

Suggested Citation

  • Z Xu & M Xia, 2014. "Iterative algorithms for improving consistency of intuitionistic preference relations," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(5), pages 708-722, May.
    • Handle: RePEc:pal:jorsoc:v:65:y:2014:i:5:p:708-722
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    Citations

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    Cited by:

    1. Wu, Zhibin & Xu, Jiuping, 2016. "Managing consistency and consensus in group decision making with hesitant fuzzy linguistic preference relations," Omega, Elsevier, vol. 65(C), pages 28-40.
    2. 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.
    3. Zhou-Jing Wang & Yuhong Wang & Kevin W. Li, 2016. "An Acceptable Consistency-Based Framework for Group Decision Making with Intuitionistic Preference Relations," Group Decision and Negotiation, Springer, vol. 25(1), pages 181-202, January.
    4. Sun, Bingzhen & Ma, Weimin, 2015. "An approach to consensus measurement of linguistic preference relations in multi-attribute group decision making and application," Omega, Elsevier, vol. 51(C), pages 83-92.
    5. Zhen Zhang & Chonghui Guo, 2017. "Deriving priority weights from intuitionistic multiplicative preference relations under group decision-making settings," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(12), pages 1582-1599, December.
    6. 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.
    7. Jia-Wei Tang & Tsuen-Ho Hsu, 2018. "Utilizing the Hierarchy Structural Fuzzy Analytical Network Process Model to Evaluate Critical Elements of Marketing Strategic Alliance Development in Mobile Telecommunication Industry," Group Decision and Negotiation, Springer, vol. 27(2), pages 251-284, April.

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