Estimating the missing values for the incomplete decision matrix and consistency optimization in emergency management

• Extend the geometric mean induced bias matrix to estimate the missing judgment.
• Optimize the missing values by the least absolute error method.
• Optimize the missing values by the least square method.
• Improve the consistency ratio of emergency decision matrix.
• Improve the emergency decision efficiency by skipping some direct comparisons.

Unconventional emergency decision making not only involves intangible and conflicting criteria, but also needs a fast response to the emergency incident under the cases of time pressure and incomplete information. It might be an effective way to make full use of the outlier data of incident information and skip some direct comparisons between alternatives to make a fast emergency decision. Focusing on the missing judgments estimation issue in an incomplete comparison emergency decision matrix, this paper extends the geometric mean induced bias matrix to estimate the missing judgments and improve the consistency ratios at the same time. The least absolute error method and the least square method are used to optimize the revised geometric mean induced bias matrix and find the missing values. A numerical example with incomplete information is used to demonstrate the proposed models. A case of emergency decision making simulation is also conducted to show how the proposed model is applied in practice. The results show the proposed models are not only capable of completing missing values, but also can efficiently improve the matrix consistency at the same time. In addition, the proposed model can aid emergency managers to make a fast response to unconventional emergency in the case of lacking complete information.