90 Then, the weight of each criterion was obtained by averaging the elements of each row of the normalized matrix ∗, according to Eq. (3). Operationally, this involves computing, for each criterion , the average of its normalized values across all criteria , yielding the priority vector =[ 1,…, ] with =6 and satisfying the normalization condition ∑ =1 =1. The resulting values correspond to the relative weights assigned to each criterion within the proposed integrated indicator framework. The final weights computed for the six criteria, along with their corresponding ranking, are reported in Table 3 in percentage terms. Table 3 - AHP weights and ranking of socio-environmental criteria Criteria Weights Ranking C1 9.84% 6 C2 19.61% 2 C3 25.69% 1 C4 12.70% 5 C5 16.64% 3 C6 15.51% 4 It is important to indicate that at this stage, the resulting group matrix represents a preliminary synthesis of expert judgment, which serves as the basis for subsequent consistency assessment and priority derivation. 4.3 Consistency of the aggregated judgment To verify the internal coherence of the pairwise comparisons, the consistency of the group matrix ˉ was evaluated using Saaty’s standard framework by reporting the maximum eigenvalue max, the CI, and the CR. The value of maxwas obtained from the matrix ˉ and used as input to compute CI according to Eq. (4). Subsequently, CI was converted into the CR using Eq. (5), where is associated with matrix size . For =6, =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 max, CI, RI, and CR are reported in Table 4. Table 4 - Consistency metrics for the group matrix ˉ . Metrics Value 6.11 CI 0.02 RI 1.24
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