PROMETHEE I: Preference Ranking Organisation METHod for Enrichment Evaluations I (partial ranking)

Overview

Outranking via positive/negative flows (partial preorder). Output typically preference_flow (higher value = preferred).

Strengths

• •Method-specific: Outranking via positive/negative flows (partial preorder)

Limitations

• •Rank reversal known on alternative-set changes (ref: general MCDM literature)
• •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

• •if d>0, P=0 otherwise. For Type III (linear): P = min(d, p_j) / p_j.
• •if φ⁺_i > φ⁺_k AND φ⁻_i < φ⁻_k.

Common pitfalls

• •Hatalı: 'PROMETHEE-I bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision-maker can specify preference (p), indifference (q), and veto (v) thresholds
• •Hatalı: 'PROMETHEE-I bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Non-compensatory preference structure
• •Hatalı: PROMETHEE-I'yi 'Small dataset (m<3) → outranking benefit minimal' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: PROMETHEE-I'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: Compute per-criterion preference degree P_j(A_i, A_k) using selected preference function type and thresholds. For Type I (usual): P=1 if d>0, P=0 otherwise. For Type III (linear): P = min(d, p_j) / p_j. Formül: d_{j}(a,b) = g_{j}(a)-g_{j}(b) \text{ (benefit)},\;g_{j}(b)-g_{j}(a) \text{ (cost)};\quad P_{j}(a,b)=H_{j}(d_{j}(a,b)) \in [0,1] Anchor: Brans et al. 1986, p.230 Table 1
2. 2.Adım 2 (F2): Step 2: Compute aggregated preference index π(A_i, A_k) = Σ_j w_j · P_j(A_i, A_k). Formül: \pi(a,b) = \sum_{j=1}^{n}w_{j}\,P_{j}(a,b) Anchor: Brans et al. 1986, p.231 Eq.(5)
3. 3.Adım 3 (F3): Step 3: Compute positive flow φ⁺(A_i) = Σ_k π(A_i, A_k)/(m−1) and negative flow φ⁻(A_i) = Σ_k π(A_k, A_i)/(m−1). For PROMETHEE I: partial ranking: A_i outranks A_k if φ⁺_i > φ⁺_k AND φ⁻_i < φ⁻_k. Formül: \phi^{+}(a) = \frac{1}{m-1}\sum_{b \neq a}\pi(a,b);\quad \phi^{-}(a) = \frac{1}{m-1}\sum_{b \neq a}\pi(b,a) Anchor: Brans et al. 1986, p.231-232 Eqs.(6)-(9)

Commonly paired with

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

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