Scoring Formula - How AHP Scores Are Computed

Calculation Method

The final AHP score for each language is computed as follows:

Normalization

For each metric i, the raw value v_ij of language j is normalized to n_ij in [0,1]:

• For higher-is-better metrics: n_ij = (v_ij - min(v_i)) / (max(v_i) - min(v_i))
• For lower-is-better metrics (ranks): n_ij = (max(v_i) - v_ij) / (max(v_i) - min(v_i))

Weighted Sum

The composite score S_j for language j is:

S_j = sum_i ( w_i * n_ij )

where w_i is the AHP-derived weight of metric i and sum_i w_i = 1.

Consistency Check

Lambda max = (1/n) * sum_i ( (A*w)_i / w_i ) CI = (lambda_max - n) / (n - 1) CR = CI / RI, where RI for n=30 is approximately 1.56. Our judgment matrix yields CR < 0.10, confirming consistency.