1682 4.3 Consistency of the aggregated judgment To verify the internal coherence of the pairwise comparisons, the consistency of the group matrix }¯ was evaluated using Saaty’s standard framework by reporting the maximum eigenvalue ÎÄÅa, the CI, and the CR. The value of ÎÄÅawas obtained from the matrix }¯ and used as input to compute CI according to Eq. (4). Subsequently, CI was converted into the CR using Eq. (5), where VZ is associated with matrix size Å. For Å=6, VZ =1.24 was used. This indicator reports consistency in a dimensionless and comparable form and is routinely used in AHP applications to document the internal validity of aggregated judgments. The resulting values of ÎÄÅa, CI, RI, and CR are reported in Table 4. Table 4 - Consistency metrics for the group matrix }¯. Metrics Value />?@ 6.11 CI 0.02 RI 1.24 CR 0.02 Since sV = 0.02 ≤ 0.10, the level of consistency is considered acceptable, indicating that the aggregated expert judgments are sufficiently coherent for deriving the priority weights. 4.4 Output for indicator structuring The weights 2)obtained through AHP allow the integrated socio-environmental risk indicator to be defined as a weighted aggregation of normalized scores (Q)for each criterion. Accordingly, the indicator is expressed as: Z =2Q! ∙ (Q! +2Q# ∙ (Q# +2QZ ∙ (QZ +2QY ∙ (QY +2Q ∙ (Q +2QÇ ∙ (QÇ (7) where 2Q!,…,2QÇ correspond to the normalized scores associated with: 2Q! à Surface disturbance, 2Q# à Extreme climate events, 2QZ à Energy consumption, 2QY à Mine-to-water-resources distance, 2Q à Mine-to-population-centers distance, and 2QÇ à Distance between water resources and population centers. Substituting the AHP weights: Z = 0.0984 ∙ ( Q! +0.1962 ∙ (Q# +0.2569 ∙ (QZ +0.1270 ∙ (QY +0.1664 ∙ (Q +0.1551 ∙ (QÇ (8) where (Q) denotes the normalized score of criterion s), obtained from the criterion assessment using quantitative and/or qualitative variables. In qualitative cases, (Q) is assigned based on a risk-level classification (e.g., low, moderate, and high) and then normalized to a common scale (e.g., 0–1) to enable weighted aggregation within the indicator. 5. DISCUSSION The AHP preliminary results show a robust and consistent prioritization of the six socioenvironmental criteria assessed, reinforcing the usefulness of the method for making priorities explicit in strategic decisions where heterogeneous dimensions converge. In particular, the dominance of energy
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