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Some Issues On Multiplicative Consistency Of Interval Reciprocal Relations

Author

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  • MEIMEI XIA

    (School of Economics and Management, Southeast University, Nanjing, Jiangsu 211189, P. R. China)

  • ZESHUI XU

    (School of Economics and Management, Southeast University, Nanjing, Jiangsu 211189, P. R. China)

Abstract

Consistency plays an important part in decision making with interval reciprocal relation also called interval fuzzy preference relation. In this paper, we give the definition of perfect multiplicative consistent interval reciprocal relation and discuss its properties. A method is proposed to construct a set of multiplicative consistent reciprocal relations from a perfect consistent interval reciprocal relation. Then we develop methods to get the perfect multiplicative consistent interval reciprocal relation from the inconsistent one and estimate the missing values from an incomplete interval reciprocal relation. Finally, a group decision-making method is proposed based on perfect multiplicative consistent interval reciprocal relations. Some examples are also given to compare the proposed methods with the existing ones.

Suggested Citation

  • Meimei Xia & Zeshui Xu, 2011. "Some Issues On Multiplicative Consistency Of Interval Reciprocal Relations," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 10(06), pages 1043-1065.
    • Handle: RePEc:wsi:ijitdm:v:10:y:2011:i:06:n:s0219622011004701
    DOI: 10.1142/S0219622011004701
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    Citations

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    Cited by:

    1. 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.
    2. Zeshui Xu & Xiaoqiang Cai, 2013. "On Consensus of Group Decision Making with Interval Utility Values and Interval Preference Orderings," Group Decision and Negotiation, Springer, vol. 22(6), pages 997-1019, November.
    3. Ting Kuo & Ming-Hui Chen, 2022. "On Indeterminacy of Interval Multiplicative Pairwise Comparison Matrix," Mathematics, MDPI, vol. 10(4), pages 1-18, February.
    4. Jana Krejčí, 2019. "On extension of multiplicative consistency to interval fuzzy preference relations," Operational Research, Springer, vol. 19(3), pages 783-815, September.
    5. Wang, Zhou-Jing & Li, Kevin W., 2015. "A multi-step goal programming approach for group decision making with incomplete interval additive reciprocal comparison matrices," European Journal of Operational Research, Elsevier, vol. 242(3), pages 890-900.

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