1680 k¯)* =…Èk) ( * +) - +/! !/- (1) Once the aggregated matrix }¯ is obtained, the global priority vector 2=[2!,2#,…,2$] is computed using Saaty’s normalized column method. First, }¯ is column-normalized as: k) ∗ * = kÍ) * ∑ kÍ& * $&/! (2) For T,Á = 1,2,3…,Å. Then, criteria weights are obtained by averaging the entries of each row of the normalized matrix: 2) = Å 1 Ck) ∗ * $ */! (3) For T =1,2,3…,Å. Which yields ∑ 2) $ )/! =1. To assess the validity of the expressed judgments, the consistency of the aggregated pairwise comparison matrix }¯ is evaluated through Saaty’s Consistency Index (CI) and Consistency Ratio (CR). Let ÎÄÅa denote the maximum eigenvalue of }¯. The Consistency Index is computed as: sZ = Î-5( Å− − 1 Å (4) Where VZ is Saaty’s Random Index for a matrix of size Å. Following common practice, judgments are considered acceptably consistent when sV≤0.10. sV= V sZ Z (5) 3.3 Structure of the integrated socio-environmental risk indicator Based on the weights 2) obtained through AHP, the structure of an integrated socio-environmental risk indicator is defined as a weighted aggregation of normalized scores for each criterion. In general terms, the indicator is expressed as: Z =C2) Ç )/! () (5) where (), represents the normalized score of criteria T. This formulation provides a transparent and replicable basis for consolidating multiple socio-environmental dimensions into an integrated measure, which can be used as an input for strategic assessments and subsequent analyses in mine planning.
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