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Studies on Interval Multiplicative Preference Relations and Their Application to Group Decision Making

Author

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  • Meimei Xia

    (Tsinghua University)

  • Jian Chen

    (Tsinghua University)

Abstract

The consistency of interval multiplicative preference relations is studied and applied to group decision making. Weak transitivity for interval multiplicative preference relation is defined by comparing two interval multiplicative preferemnce values using a possibility degree formula. The consistent interval multiplicative preference relation is defined based on interval operations, which provides a convenient means to check whether an interval multiplicative preference relation is consistent. A goal-programming model is established to derive the interval priority weight vector from an interval multiplicative preference relation, which must solve only one model. An algorithm is developed through interaction with decision makers to ensure the transitivity of an interval multiplicative preference relation. The proposed methods are then extended to deal with incomplete interval multiplicative preference relations, which can determine the priority weight vector without estimating missing values. An algorithm is also developed to derive the priority vector from group multiplicative preference relations. This algorithm can help decision makers ensure the weak transitivity of their provided multiplicative preference relations.

Suggested Citation

  • Meimei Xia & Jian Chen, 2015. "Studies on Interval Multiplicative Preference Relations and Their Application to Group Decision Making," Group Decision and Negotiation, Springer, vol. 24(1), pages 115-144, January.
    • Handle: RePEc:spr:grdene:v:24:y:2015:i:1:d:10.1007_s10726-014-9383-9
    DOI: 10.1007/s10726-014-9383-9
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    References listed on IDEAS

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    2. 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.
    3. Huimin Zhang & Meng Li & Wen Chen, 2023. "Assessing Competitiveness in New Energy Vehicle Enterprises: A Group Decision Model with Interval Multiplicative Preference Relations," Mathematics, MDPI, vol. 12(1), pages 1-21, December.
    4. Meng, Fanyong & Xiong, Beibei, 2021. "Logical efficiency decomposition for general two-stage systems in view of cross efficiency," European Journal of Operational Research, Elsevier, vol. 294(2), pages 622-632.
    5. Pedro Huidobro & Pedro Alonso & Vladimír Janiš & Susana Montes, 2022. "Convexity and level sets for interval-valued fuzzy sets," Fuzzy Optimization and Decision Making, Springer, vol. 21(4), pages 553-580, December.
    6. Jian Li & Jian-qiang Wang & Jun-hua Hu, 2019. "Interval-valued n-person cooperative games with satisfactory degree constraints," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(4), pages 1177-1194, December.
    7. Ting Kuo & Ming-Hui Chen, 2022. "On Indeterminacy of Interval Multiplicative Pairwise Comparison Matrix," Mathematics, MDPI, vol. 10(4), pages 1-18, February.
    8. Liu Fang & Peng Yanan & Zhang Weiguo & Pedrycz Witold, 2017. "On Consistency in AHP and Fuzzy AHP," Journal of Systems Science and Information, De Gruyter, vol. 5(2), pages 128-147, April.
    9. Gong, Zaiwu & Guo, Weiwei & Herrera-Viedma, Enrique & Gong, Zejun & Wei, Guo, 2020. "Consistency and consensus modeling of linear uncertain preference relations," European Journal of Operational Research, Elsevier, vol. 283(1), pages 290-307.
    10. 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.
    11. Fu, Chao & Chang, Wenjun & Xue, Min & Yang, Shanlin, 2019. "Multiple criteria group decision making with belief distributions and distributed preference relations," European Journal of Operational Research, Elsevier, vol. 273(2), pages 623-633.

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