ELECTRE I: ELimination Et Choix Traduisant la REalité I (kernel / choice)

Overview

Outranking: concordance/discordance with kernel extraction. Output typically preference_flow (higher value = preferred).

Strengths

• •Method-specific: Outranking: concordance/discordance with kernel extraction

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-I-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

• •Hatalı: 'ELECTRE-I bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision-maker can specify preference (p), indifference (q), and veto (v) thresholds
• •Hatalı: 'ELECTRE-I bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Non-compensatory preference structure
• •Hatalı: ELECTRE-I'yi 'Small dataset (m<3) → outranking benefit minimal' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: ELECTRE-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: Vector normalisation of decision matrix. Formül: r_{ij} = \dfrac{x_{ij}}{\sqrt{\sum_{k} x_{kj}^{2}}} Anchor: Roy 1968, p.61 Eq.(1)
2. 2.Adım 2 (F2): Step 2: Weighted normalised matrix v_ij = w_j r_ij. Formül: v_{ij} = w_{j}\,r_{ij} Anchor: Roy 1968, p.61 Eq.(2)
3. 3.Adım 3 (F3): Step 3: Concordance index C(a,b) = Σ_{j: Δ_j(a,b)≥0} w_j. 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} Anchor: Roy 1968, p.62 Eq.(3)
4. 4.Adım 4 (F4): Step 4: Discordance index D(a,b) = max(-Δ_j(a,b))/max|v_kj−v_lj|. Formül: D(a,b) = \dfrac{\max_{\{j: \Delta_{j}(a,b)<0\}}\bigl(-\Delta_{j}(a,b)\bigr)}{\max_{k,l,j}|v_{kj}-v_{lj}|},\quad \Delta_{j}(a,b) = \begin{cases} v_{aj}-v_{bj} & j\in J^{+} \\ v_{bj}-v_{aj} & j\in J^{-} \end{cases} Anchor: Roy 1968, p.62 Eq.(4)
5. 5.Adım 5 (F5): Step 5: Concordance/discordance thresholds c̄ and d̄. Formül: \bar{c} = \dfrac{1}{m(m-1)}\sum_{a\neq b} C(a,b),\quad \bar{d} = \dfrac{1}{m(m-1)}\sum_{a\neq b} D(a,b) Anchor: Roy 1968, p.63 Eqs.(5)-(6)
6. 6.Adım 6 (F6): Step 6: Outranking relation a S b ⟺ C(a,b)≥c̄ AND D(a,b)≤d̄; kernel via graph. Formül: a\,S\,b \iff C(a,b)\ge \bar{c}\ \text{AND}\ D(a,b)\le \bar{d} Anchor: Roy 1968, p.63 Eq.(7)

Commonly paired with

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

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