88 ˉ =(∏ ( ) =1 ) 1/ (1) Once the aggregated matrix ˉ is obtained, the global priority vector =[ 1, 2,…, ] is computed using Saaty’s normalized column method. First, ˉ is column-normalized as: ∗ = ̅ ∑ ̅ =1 (2) For , = 1,2,3 … , . Then, criteria weights are obtained by averaging the entries of each row of the normalized matrix: = 1 ∑ ∗ =1 (3) For = 1,2,3 … , . Which yields ∑ =1 =1. To assess the validity of the expressed judgments, the consistency of the aggregated pairwise comparison matrix ˉ is evaluated through Saaty’s Consistency Index (CI) and Consistency Ratio (CR). Let max denote the maximum eigenvalue of ˉ . The Consistency Index is computed as: = − −1 (4) Where is Saaty’s Random Index for a matrix of size . Following common practice, judgments are considered acceptably consistent when ≤0.10. = (5) 3.3 Structure of the integrated socio-environmental risk indicator
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