PROMETHEE II: Preference Ranking Organisation METHod for Enrichment of Evaluations

Overview

Preference function (net flow). Output typically preference_flow (higher value = preferred).

Strengths

• •Method-specific: Preference function (net flow)

Limitations

• •Rank reversal known on alternative-set changes (ref: Brans & Mareschal 2005 §4 (mild))
• •Assumes: Decision-maker can specify preference (p), indifference (q), and veto (v) thresholds
• •Assumes: Non-compensatory preference structure

Assumptions to verify

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

When not to use

• •Small dataset (m<3) → outranking benefit minimal
• •Compensatory preferences acceptable → simpler ranking method

Edge cases

• •See F.steps and D.parameters for PROMETHEE-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

• •Hatalı: 'PROMETHEE bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision-maker can specify preference (p), indifference (q), and veto (v) thresholds
• •Hatalı: 'PROMETHEE bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Non-compensatory preference structure
• •Hatalı: PROMETHEE'yi 'Small dataset (m<3) → outranking benefit minimal' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: PROMETHEE'yi 'Compensatory preferences acceptable → simpler ranking method' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Choose preference function P_j and parameters (q,p) per criterion (d_j direction-aware). Formül: d_{j}(a,b) = \begin{cases} x_{aj}-x_{bj} & j\in J^{+} \\ x_{bj}-x_{aj} & j\in J^{-} \end{cases};\quad P_{j}(d): \mathbb{R}\to[0,1] Anchor: Brans-Vincke 1985, p.649 Eq.(2)
2. 2.Adım 2 (F2): Step 2: Pairwise preference π(a,b) = Σ w_j P_j(d_j(a,b)). Formül: \pi(a,b) = \sum_{j=1}^{n} w_{j}\,P_{j}\bigl(d_{j}(a,b)\bigr) Anchor: Brans-Mareschal 2002, p.41 Eq.(5)
3. 3.Adım 3 (F3): Step 3: Positive flow φ^+(a) = (1/(m-1)) Σ_b π(a,b). Formül: \phi^{+}(a) = \dfrac{1}{m-1} \sum_{b\neq a} \pi(a,b) Anchor: Brans-Mareschal 2002, p.41 Eq.(6)
4. 4.Adım 4 (F4): Step 4: Negative flow φ^−(a) = (1/(m-1)) Σ_b π(b,a). Formül: \phi^{-}(a) = \dfrac{1}{m-1} \sum_{b\neq a} \pi(b,a) Anchor: Brans-Mareschal 2002, p.41 Eq.(7)
5. 5.Adım 5 (F5): Step 5: Net flow φ(a) = φ^+(a) − φ^−(a); descending complete ranking (PROMETHEE II). Formül: \phi(a) = \phi^{+}(a) - \phi^{-}(a) Anchor: Brans-Mareschal 2002, p.41 Eq.(8)

Commonly paired with

• •AHP + PROMETHEE (high)
• •BWM + PROMETHEE (high)
• •ENTROPY + PROMETHEE (high)
• •CRITIC + PROMETHEE (high)
• •SWARA + PROMETHEE (high)

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