ELECTRE III: ELimination Et Choix Traduisant la REalité III (pseudo-criteria, fuzzy outranking)

Overview

Fuzzy outranking with indifference/preference/veto thresholds (complete preorder). Output typically preference_flow (higher value = preferred).

Strengths

• •Method-specific: Fuzzy outranking with indifference/preference/veto 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-III-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

• •Hatalı: 'ELECTRE-III bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision-maker can specify preference (p), indifference (q), and veto (v) thresholds
• •Hatalı: 'ELECTRE-III bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Non-compensatory preference structure
• •Hatalı: ELECTRE-III'yi 'Small dataset (m<3) → outranking benefit minimal' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: ELECTRE-III'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: Three thresholds per criterion: indifference q_j, preference p_j, veto v_j. Formül: 0 \le q_{j} \le p_{j} \le v_{j} Anchor: Roy 1978, p.244 Sec.3
2. 2.Adım 2 (F2): Step 2: Per-criterion concordance c_j(a,b) using fuzzy thresholds q,p (direction-aware Δ_j). Formül: \Delta_{j}(a,b) = \begin{cases} x_{bj}-x_{aj} & j\in J^{+} \\ x_{aj}-x_{bj} & j\in J^{-} \end{cases}; \quad c_{j}(a,b) = \begin{cases} 1 & \Delta_{j}(a,b)\le q_{j} \\ 0 & \Delta_{j}(a,b)\ge p_{j} \\ \dfrac{p_{j}-\Delta_{j}(a,b)}{p_{j}-q_{j}} & \text{else}\end{cases} Anchor: Roy 1978, p.245 Eq.(1)
3. 3.Adım 3 (F3): Step 3: Comprehensive concordance C(a,b) = Σ w_j c_j(a,b). Formül: C(a,b) = \sum_{j=1}^{n} w_{j}\,c_{j}(a,b) Anchor: Roy 1978, p.245 Eq.(2)
4. 4.Adım 4 (F4): Step 4: Per-criterion discordance d_j(a,b) using veto v_j (direction-aware Δ_j). Formül: d_{j}(a,b) = \begin{cases} 0 & \Delta_{j}(a,b)\le p_{j} \\ 1 & \Delta_{j}(a,b)\ge v_{j} \\ \dfrac{\Delta_{j}(a,b)-p_{j}}{v_{j}-p_{j}} & \text{else}\end{cases} Anchor: Roy 1978, p.246 Eq.(3)
5. 5.Adım 5 (F5): Step 5: Credibility σ(a,b) = C · Π (1−d_j)/(1−C) over criteria with d_j > C. Formül: \sigma(a,b) = C(a,b) \prod_{\{j: d_{j}(a,b)>C(a,b)\}} \dfrac{1 - d_{j}(a,b)}{1 - C(a,b)} Anchor: Roy 1978, p.246 Eq.(4)
6. 6.Adım 6 (F6): Step 6: Distillation procedures (descending + ascending) build two complete preorders. Formül: \text{Descending: }\sigma_{\max}-\delta(\sigma_{\max});\quad \text{Ascending: reverse direction} Anchor: Roy 1978, p.247 Sec.4
7. 7.Adım 7 (F7): Step 7: Final partial preorder = intersection of descending and ascending. Formül: \succeq^{\text{final}} = \succeq^{d} \cap \succeq^{a} Anchor: Roy 1978, p.248

Commonly paired with

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

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