ELECTRE II: ELimination Et Choix Traduisant la REalité II (complete ranking)

Overview

Outranking with strong/weak concordance thresholds (complete preorder). Output typically preference_flow (higher value = preferred).

Strengths

• •Method-specific: Outranking with strong/weak concordance thresholds (complete 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

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

Common pitfalls

• •Hatalı: 'ELECTRE-II bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision-maker can specify preference (p), indifference (q), and veto (v) thresholds
• •Hatalı: 'ELECTRE-II bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Non-compensatory preference structure
• •Hatalı: ELECTRE-II'yi 'Small dataset (m<3) → outranking benefit minimal' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: ELECTRE-II'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: Concordance C(a,b) and discordance D(a,b) indices (same as ELECTRE I). Formül: \Delta_{j}(a,b) = \begin{cases} v_{aj}-v_{bj} & j\in J^{+} \\ v_{bj}-v_{aj} & j\in J^{-} \end{cases};\quad C(a,b)=\sum_{\{j:\Delta_{j}(a,b)\ge 0\}} w_{j};\quad D(a,b)=\max_{j}\bigl(-\Delta_{j}(a,b)\bigr)/\Delta Anchor: Roy-Bertier 1973, p.4 Eqs.(1)-(2)
2. 2.Adım 2 (F2): Step 2: Strong outranking thresholds c⁺, d⁺ and weak c⁻, d⁻ define a S^F b and a S^f b. Formül: a\,S^{F}\,b \iff C\ge c^{+},D\le d^{+};\quad a\,S^{f}\,b \iff C\ge c^{-},D\le d^{-} Anchor: Roy-Bertier 1973, p.6 Eqs.(3)-(4)
3. 3.Adım 3 (F3): Step 3: Construct strong graph G^F and weak graph G^f from outranking relations. Formül: G^{F}=(\mathcal{A},S^{F}),\quad G^{f}=(\mathcal{A},S^{f}) Anchor: Roy-Bertier 1973, p.7
4. 4.Adım 4 (F4): Step 4: Direct (descending) preorder by removing strongly-dominated alternatives iteratively. Formül: V_{1}^{d}=\{a:\text{no }b\,S^{F}\,a\},\ V_{2}^{d}=V_{1}^{d}\setminus\{\text{newly dominated}\},\ldots Anchor: Roy-Bertier 1973, p.8 Procedure A1
5. 5.Adım 5 (F5): Step 5: Inverse (ascending) preorder by reversing relations. Formül: V^{a}_{k}\ \text{built on reverse outranking} Anchor: Roy-Bertier 1973, p.8 Procedure A2
6. 6.Adım 6 (F6): Step 6: Median preorder is the average of direct and inverse preorders. Formül: V^{m}_{i} = \dfrac{V^{d}_{i} + V^{a}_{i}}{2} Anchor: Roy-Bertier 1973, p.8 Procedure A3
7. 7.Adım 7 (F7): Step 7: Final ranking from median preorder. Formül: \text{rank}(A_{i})=\lceil V^{m}_{i}\rceil Anchor: Roy-Bertier 1973, p.9

Commonly paired with

• •AHP + ELECTRE-II (high)
• •BWM + ELECTRE-II (high)
• •ENTROPY + ELECTRE-II (high)
• •CRITIC + ELECTRE-II (high)
• •SWARA + ELECTRE-II (high)

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