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Multiple attribute decision-making method based on projection model for dual hesitant fuzzy set

Author

Listed:
  • Yan Ni

    (Army Engineering University of PLA)

  • Hua Zhao

    (Army Engineering University of PLA)

  • Zeshui Xu

    (Sichuan University)

  • Zeyan Wang

    (Army Engineering University of PLA)

Abstract

In the decision-making process, retaining the original data information has become a most crucial step. Dual hesitant fuzzy sets (DHFS), which can reflect the original membership degree and non-membership degree information given by the DMs, is a kind of new tool for the DMs to provide the original information as much as possible. In this paper, we focus on the decision- making problem by a projection model (Algorithm I) whose attribute values are given in the forms of dual hesitant fuzzy elements (DHFEs). In order to reflect the information of the data more accurately, we first divide the dual hesitant fuzzy decision matrix into membership degree matrix and non-membership degree matrix. Then we gain the virtual positive ideal solution from the membership degree matrix and the negative positive ideal solution from the non-membership degree matrix. And then the projection values from every solution to the virtual positive ideal solution and the negative positive ideal solution are calculated. In combination with the two projection values, the relative consistent degree is further calculated to rank all the alternatives. At the same time, in order to guarantee the rationality of the decision-making result, a variation coefficient method is developed to determine the weights of the attributes under dual hesitant fuzzy environment objectively. Finally, the existing algorithms (Algorithm II and Algorithm III, Algorithm IV, Algorithm V) are compared with our algorithm (Algorithm I). The comparison result shows that Algorithm I is a valuable tool for decision making.

Suggested Citation

  • Yan Ni & Hua Zhao & Zeshui Xu & Zeyan Wang, 2022. "Multiple attribute decision-making method based on projection model for dual hesitant fuzzy set," Fuzzy Optimization and Decision Making, Springer, vol. 21(2), pages 263-289, June.
    • Handle: RePEc:spr:fuzodm:v:21:y:2022:i:2:d:10.1007_s10700-021-09366-9
    DOI: 10.1007/s10700-021-09366-9
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    References listed on IDEAS

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    1. Zeshui Xu & Qingli Da, 2004. "Projection Method For Uncertain Multi-Attribute Decision Making With Preference Information On Alternatives," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 429-434.
    2. Bin Zhu & Zeshui Xu & Meimei Xia, 2012. "Dual Hesitant Fuzzy Sets," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, May.
    3. Opricovic, Serafim & Tzeng, Gwo-Hshiung, 2004. "Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS," European Journal of Operational Research, Elsevier, vol. 156(2), pages 445-455, July.
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