Ranking method · Saaty, 1977

Classical AHP

Analytic Hierarchy Process synthesis ranking

Ranks alternatives from criteria comparisons plus alternative comparisons under every criterion.

How it works

1. Compare criteria pairwise on the Saaty 1–9 scale.
2. For each criterion, compare the alternatives pairwise on the same scale.
3. Derive one criteria priority vector and one local alternative priority vector per criterion.
4. Synthesize final scores by multiplying local priorities by criteria weights and summing across criteria.
5. Check the Consistency Ratio for every matrix; any CR ≥ 0.10 blocks the ranking.

Use it when

• The decision is mainly judgment-based and the raw performance matrix does not capture the trade-offs well.
• Experts can compare alternatives directly under each criterion.
• You want a classical Saaty AHP hierarchy rather than AHP weights feeding another MCDM ranking method.

Watch out for

• It uses subjective pairwise judgments, so it is not directly comparable with methods that rank the numeric decision matrix.
• The number of comparisons grows quickly: n alternatives require n(n−1)/2 judgments under each criterion.
• Use AHP-specific sensitivity rather than numeric data perturbation for robustness claims.

Parameters

Criteria matrix plus one alternatives matrix per criterion; all CR values must stay below 0.10.

Cite the method

Saaty, T. L. (1980). The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation. McGraw-Hill.

@book{saaty1980ahp,
  author    = {Saaty, Thomas L.},
  title     = {The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation},
  publisher = {McGraw-Hill},
  address   = {New York},
  year      = {1980}
}