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On Consensus of Group Decision Making with Interval Utility Values and Interval Preference Orderings

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  • Zeshui Xu

    (PLA University of Science and Technology)

  • Xiaoqiang Cai

    (The Chinese University of Hong Kong)

Abstract

Uncertainty is a common phenomenon in our real world. Interval utility values and interval preference orderings are two of the simplest and most convenient tools to describe uncertain preferences in decision making. In this paper, we investigate consensus problems in group decision making with interval utility values and interval preference orderings. We first establish their transformation relations, and give a formula for calculating the association coefficients of individual uncertain preferences and group ones. We then develop a consensus procedure for group decision making with interval utility values and interval preference orderings, which takes interval utility values as the uniform preference representation. This procedure can be reduced to a series of processes for dealing with some special group decision making situations, such as: group decision making with utility values and preference orderings, group decision making with interval utility values, group decision making with interval preference orderings, etc. Finally, we illustrate the applications of the developed procedures with two practical examples.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:grdene:v:22:y:2013:i:6:d:10.1007_s10726-012-9298-2
    DOI: 10.1007/s10726-012-9298-2
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    References listed on IDEAS

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    1. Samuel E. Bodily, 1979. "Note--A Delegation Process for Combining Individual Utility Functions," Management Science, INFORMS, vol. 25(10), pages 1035-1041, October.
    2. Haines, Linda M., 1998. "A statistical approach to the analytic hierarchy process with interval judgements. (I). Distributions on feasible regions," European Journal of Operational Research, Elsevier, vol. 110(1), pages 112-125, October.
    3. Herrera, F. & Herrera-Viedma, E. & Chiclana, F., 2001. "Multiperson decision-making based on multiplicative preference relations," European Journal of Operational Research, Elsevier, vol. 129(2), pages 372-385, March.
    4. Xu, Zeshui & Chen, Jian, 2008. "Some models for deriving the priority weights from interval fuzzy preference relations," European Journal of Operational Research, Elsevier, vol. 184(1), pages 266-280, January.
    5. 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.
    6. Zeshui Xu & Xiaoqiang Cai, 2012. "Uncertain Power Average Operators for Aggregating Interval Fuzzy Preference Relations," Group Decision and Negotiation, Springer, vol. 21(3), pages 381-397, May.
    7. 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.
    8. Horace W. Brock, 1980. "The Problem of “Utility Weights” in Group Preference Aggregation," Operations Research, INFORMS, vol. 28(1), pages 176-187, February.
    9. Ramanathan, R. & Ganesh, L. S., 1994. "Group preference aggregation methods employed in AHP: An evaluation and an intrinsic process for deriving members' weightages," European Journal of Operational Research, Elsevier, vol. 79(2), pages 249-265, December.
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    Cited by:

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    5. Jianjun Zhu & Shitao Zhang & Ye Chen & Lili Zhang, 2016. "A Hierarchical Clustering Approach Based on Three-Dimensional Gray Relational Analysis for Clustering a Large Group of Decision Makers with Double Information," Group Decision and Negotiation, Springer, vol. 25(2), pages 325-354, March.

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