PROMETHEE II: Preference Ranking Organisation Method for Enrichment of Evaluations II

Overview

Outranking (pairwise preference flows: complete ranking). Output typically net_flow (higher value = preferred).

Strengths

• •Method-specific: Outranking (pairwise preference flows: complete ranking)

Limitations

• •Rank reversal known on alternative-set changes (ref: Mareschal et al. 2008 (IEEE IEEM))
• •Assumes: Decision-maker can specify appropriate preference function type per criterion
• •Assumes: Criteria are measured on commensurate or comparable scales
• •Assumes: Rank reversal is acceptable (or use SPOTIS/RAFSI if it is not)

Assumptions to verify

• •Decision-maker can specify appropriate preference function type per criterion
• •Criteria are measured on commensurate or comparable scales
• •Rank reversal is acceptable (or use SPOTIS/RAFSI if it is not)

When not to use

• •Rank reversal is unacceptable: use SPOTIS or RAFSI instead
• •Very large alternative sets (m > 50): O(m²) pairwise comparisons become expensive
• •Purely compensatory aggregation needed: use TOPSIS or WASPAS

Edge cases

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

Common pitfalls

• •Hatalı: 'PROMETHEE_II bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision-maker can specify appropriate preference function type per criterion
• •Hatalı: 'PROMETHEE_II bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria are measured on commensurate or comparable scales
• •Hatalı: 'PROMETHEE_II bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Rank reversal is acceptable (or use SPOTIS/RAFSI if it is not)
• •Hatalı: PROMETHEE_II'yi 'Rank reversal is unacceptable' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: PROMETHEE_II'yi 'Very large alternative sets (m > 50)' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: PROMETHEE_II'yi 'Purely compensatory aggregation needed' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: For each criterion j, compute pairwise difference matrix d_j(a,b): benefit criteria → x_aj − x_bj; cost criteria → x_bj − x_aj. Formül: d_{j}(a,b) = \begin{cases} x_{aj} - x_{bj} & j \in J^{+}\\ x_{bj} - x_{aj} & j \in J^{-} \end{cases} Anchor: Brans & Vincke 1985, p.649 Eq.(1)
2. 2.Adım 2 (F2): Step 2: Apply preference function F_j to each pairwise difference to get unicriterion preference degree P_j(a,b) ∈ [0,1]. Common types: usual (0/1), vshape (linear ramp), ushape (step at q), level (combines p and q), vshape_2 (linear with q cutoff). Formül: P_{j}(a,b) = F_{j}\bigl(d_{j}(a,b)\bigr) \in [0,1] Anchor: Brans & Vincke 1985, p.649-650 Table 1 (6 preference functions)
3. 3.Adım 3 (F3): Step 3: Aggregate unicriterion preferences into global pairwise preference index π(a,b) = Σ_j w_j · P_j(a,b). Formül: \pi(a,b) = \sum_{j=1}^{n} w_{j}\,P_{j}(a,b) Anchor: Brans & Vincke 1985, p.650 Eq.(2)
4. 4.Adım 4 (F4): Step 4: Compute positive outranking flow Φ⁺(a) and negative outranking flow Φ⁻(a). Formül: \Phi^{+}(a) = \dfrac{1}{m-1}\sum_{b \neq a} \pi(a,b),\qquad \Phi^{-}(a) = \dfrac{1}{m-1}\sum_{b \neq a} \pi(b,a) Anchor: Brans et al. 1986, p.230 Eqs.(2)-(3)
5. 5.Adım 5 (F5): Step 5: Net flow Φ(a) = Φ⁺(a) − Φ⁻(a). Rank descending (higher net flow = better). Complete ranking (PROMETHEE II, as opposed to partial PROMETHEE I). Formül: \Phi(a) = \Phi^{+}(a) - \Phi^{-}(a),\quad \text{rank descending} Anchor: Brans et al. 1986, p.231 Eq.(4)

Commonly paired with

• •AHP + PROMETHEE_II (high)
• •BWM + PROMETHEE_II (medium)
• •CRITIC + PROMETHEE_II (medium)
• •ENTROPY + PROMETHEE_II (medium)

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