Ranking method · Brans, 1982

PROMETHEE

Preference Ranking Organization METHod for Enrichment of Evaluations (I & II)

Compares alternatives pairwise with preference functions, so small differences don't get over-rewarded.

How it works

1. For every pair of alternatives and every criterion, translate the performance difference into a preference degree (0–1) using a per-criterion preference function (usual, U-shape, V-shape, level, linear, or Gaussian).
2. Aggregate the weighted preference degrees into a matrix π(a, b).
3. Compute the leaving flow Φ⁺ (how strongly a beats the others), entering flow Φ⁻ (how strongly it is beaten), and net flow Φ = Φ⁺ − Φ⁻.
4. PROMETHEE I gives a partial ranking from Φ⁺/Φ⁻; PROMETHEE II ranks completely by net Φ.
5. The GAIA plane (a PCA of the per-criterion flows) shows which criteria agree, conflict, and favor which alternatives.

Use it when

• Differences below some threshold shouldn't count indifference and preference zones matter.
• Criteria are measured in incomparable units and you want to avoid aggressive normalization.
• You want the GAIA visual to communicate the trade-off structure.

Watch out for

• Choosing preference functions and their q/p/s thresholds per criterion requires thought.
• Net flow (PROMETHEE II) can hide incomparabilities that PROMETHEE I would expose.

Parameters

Per criterion: a preference function plus q (indifference), p (preference) or s (Gaussian midpoint) thresholds.

Cite the method

Brans, J.-P., & Vincke, P. (1985). A preference ranking organisation method: The PROMETHEE method for MCDM. Management Science, 31(6), 647-656.

@article{brans1985preference,
  author  = {Brans, Jean-Pierre and Vincke, Philippe},
  title   = {A preference ranking organisation method: The {PROMETHEE} method for {MCDM}},
  journal = {Management Science},
  volume  = {31},
  number  = {6},
  pages   = {647656},
  year    = {1985},
  doi     = {10.1287/mnsc.31.6.647}
}