PROMETHEE III - Preference Ranking Organisation METHod for Enrichment Evaluations III (interval ranking)

Outranking via interval flows derived from net-flow mean and dispersion

Brans, J. P., Vincke, P., Mareschal, B.1986doi:10.1016/0377-2217(86)90044-5 ↗

Overview

PROMETHEE III sits between PROMETHEE I (partial preorder) and PROMETHEE II (complete preorder): it returns a weak order built from per-alternative confidence intervals around the net flow. Tune α to control how much dispersion is admitted as indifference - small α ⇒ ranking close to PROMETHEE II; large α ⇒ many ties (indifferences) like PROMETHEE I.

Output: preference flow, higher is better
Data: Crisp, complete numeric matrix
Weights: Needs a weight source
Size: 2+ alternatives, 3-12 criteria works best
Used for: Complex multi-stakeholder decisions

Look elsewhere when

•Small dataset (m<3). Outranking benefit minimal.
•Compensatory preferences acceptable. Simpler ranking method.

Assumptions to verify

Decision-maker can specify preference (p), indifference (q), and veto (v) thresholds
Non-compensatory preference structure

Edge cases and pitfalls

Mis-applying the m vs m−1 divisor: PROMETHEE III's φ̄ uses 1/m (over all i', including the i'=i zero term), whereas PROMETHEE I/II's φ⁺/φ⁻ use 1/(m−1).
Treating α as a robustness sweep parameter rather than a fixed user choice: α should be set once per study (literature defaults are in [0.10, 0.30]) and reported alongside the ranking.

Works with

Commonly takes its weights from

AHP BWM ENTROPY CRITIC SWARA

How to cite

Brans, J. P.; Vincke, P.; Mareschal, B. (1986). How to select and how to rank projects: The PROMETHEE method. European Journal of Operational Research. https://doi.org/10.1016/0377-2217(86)90044-5

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System ID, as it appears in reports and the API

PROMETHEE-III

Overview

Output

preference flow, higher is better

Data

Crisp, complete numeric matrix

Weights

Needs a weight source

Size

2+ alternatives, 3-12 criteria works best

Used for

Complex multi-stakeholder decisions

Edge cases and pitfalls

Mis-applying the m vs m−1 divisor: PROMETHEE III's φ̄ uses 1/m (over all i', including the i'=i zero term), whereas PROMETHEE I/II's φ⁺/φ⁻ use 1/(m−1).

Treating α as a robustness sweep parameter rather than a fixed user choice: α should be set once per study (literature defaults are in [0.10, 0.30]) and reported alongside the ranking.