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Compatibility Analysis of Intuitionistic Fuzzy Preference Relations in Group Decision Making

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  • Zeshui Xu

    (Southeast University
    PLA University of Science and Technology)

Abstract

Compatibility analysis is an efficient and important tool used to measure the consensus of opinions within a given group of individuals. In this paper, we give a compatibility measure between intuitionistic preference values and a compatibility measure between intuitionistic preference relations, respectively, and study their properties. It is shown that each individual intuitionistic preference relation and the collective intuitionistic preference relation is perfectly compatible if and only if all the individual intuitionistic preference relations are perfectly compatible. Based on the compatibility measures, a consensus reaching procedure in group decision making with intuitionistic preference relations is developed, and a method for comparing intuitionistic fuzzy values is pointed out, by which the considered objects are ranked and selected. In addition, we extend the developed measures, procedure and method to accommodate group decision making situations with interval-valued intuitionistic preference relations. Numerical analysis on our results through an illustrative example is also carried out.

Suggested Citation

  • Zeshui Xu, 2013. "Compatibility Analysis of Intuitionistic Fuzzy Preference Relations in Group Decision Making," Group Decision and Negotiation, Springer, vol. 22(3), pages 463-482, May.
    • Handle: RePEc:spr:grdene:v:22:y:2013:i:3:d:10.1007_s10726-011-9278-y
    DOI: 10.1007/s10726-011-9278-y
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    References listed on IDEAS

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    1. Saaty, Thomas L. & Vargas, Luis G., 1987. "Uncertainty and rank order in the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 32(1), pages 107-117, October.
    2. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
    3. Xu, Zeshui, 2005. "Deviation measures of linguistic preference relations in group decision making," Omega, Elsevier, vol. 33(3), pages 249-254, June.
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    Cited by:

    1. Elena Rokou & Konstantinos Kirytopoulos, 2014. "A Calibrated Group Decision Process," Group Decision and Negotiation, Springer, vol. 23(6), pages 1369-1384, November.
    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. Jian Wu, 2016. "Consistency in MCGDM Problems with Intuitionistic Fuzzy Preference Relations Based on an Exponential Score Function," Group Decision and Negotiation, Springer, vol. 25(2), pages 399-420, March.
    5. Xiayu Tong & Zhou-Jing Wang, 2016. "A Group Decision Framework with Intuitionistic Preference Relations and Its Application to Low Carbon Supplier Selection," IJERPH, MDPI, vol. 13(9), pages 1-16, September.
    6. Fujun Hou, 2015. "A Consensus Gap Indicator and Its Application to Group Decision Making," Group Decision and Negotiation, Springer, vol. 24(3), pages 415-428, May.

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