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Logarithm Compatibility of Interval Multiplicative Preference Relations with an Application to Determining the Optimal Weights of Experts in the Group Decision Making

Author

Listed:
  • Yulan Wang

    (Anhui Economic Management Institute
    SUNY Canton)

  • Huayou Chen

    (Anhui University)

  • Ligang Zhou

    (Anhui University)

Abstract

We propose the new compatibility of interval multiplicative preference relations (IMPRs) in the group decision making (GDM) and apply it to determine the weights of experts. Firstly, we introduce the operation of interval numbers and define the new conception of logarithm compatibility degree of two interval multiplicative preference relations. Then, we prove the properties of logarithm compatibility of IMPR. It is pointed that if IMPR provided by every expert and its characteristic matrix are of acceptable compatibility, then the synthetic preference relation and the synthetic characteristic matrix are also of acceptable compatibility. Furthermore, we construct a mathematical programming model to determine the optimal weights of experts by minimizing the square logarithm compatibility in the GDM with IMPR and discuss the solution to the model. Finally, a numerical example is illustrated to show that the model is feasible.

Suggested Citation

  • Yulan Wang & Huayou Chen & Ligang Zhou, 2013. "Logarithm Compatibility of Interval Multiplicative Preference Relations with an Application to Determining the Optimal Weights of Experts in the Group Decision Making," Group Decision and Negotiation, Springer, vol. 22(4), pages 759-772, July.
    • Handle: RePEc:spr:grdene:v:22:y:2013:i:4:d:10.1007_s10726-012-9291-9
    DOI: 10.1007/s10726-012-9291-9
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    References listed on IDEAS

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