Analytic network process in risk assessment and decision analysis

In risk assessment and decision analysis, the analytical network process (ANP) is widely used to assess the key factors of risks and analyze the impacts and preferences of decision alternatives. There are lots of comparison matrices for a complicated risk assessment problem, but a decision has to be made rapidly in emergency cases. However, in the ANP, the reciprocal pairwise comparison matrices (RPCM) are more complicated and difficult than AHP. The consistency test and the inconsistent elements identification need to be simplified. In this paper, a maximum eigenvalue threshold is proposed as the consistency index for the ANP in risk assessment and decision analysis. The proposed threshold is mathematically equivalent to the consistency ratio (CR). To reduce the times of consistency test, a block diagonal matrix is introduced for the RPCM to conduct consistency tests simultaneously for all comparison matrices. Besides, the inconsistent elements can be identified and adjusted by an induced bias block diagonal comparison matrix. The effectiveness and the simplicity of the proposed maximum eigenvalue threshold consistency test method and the inconsistency identification and adjustment method are shown by two illustrative examples of emergent situations.