EXPROM I: Extended PROMETHEE (partial)

Overview

Outranking with weak+strong preferences. Output typically preference_flow (higher value = preferred).

Strengths

• •Method-specific: Outranking with weak+strong preferences

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

Common pitfalls

• •Hatalı: 'EXPROM-I bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision-maker can specify preference (p), indifference (q), and veto (v) thresholds
• •Hatalı: 'EXPROM-I bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Non-compensatory preference structure
• •Hatalı: EXPROM-I'yi 'Small dataset (m<3) → outranking benefit minimal' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: EXPROM-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: Pairwise differences d_j(A_i,A_l) and weak preference function P^w_j(d). Formül: d_{j}(A_{i},A_{l}) = C_{j}(A_{i}) - C_{j}(A_{l}),\quad P^{w}_{j}(d) \in [0,1] Anchor: Diakoulaki-Koumoutsos 1991, p.4 Eq.(1)
2. 2.Adım 2 (F2): Step 2: Weak preference index π^w(A_i,A_l) = Σ w_j P^w_j(A_i,A_l). Formül: \pi^{w}(A_{i},A_{l}) = \sum_{j=1}^{n} P^{w}_{j}(A_{i},A_{l})\,w_{j} Anchor: Diakoulaki-Koumoutsos 1991, p.5 Eq.(2)
3. 3.Adım 3 (F3): Step 3: Strong preference function P^s_j(d) capturing decisive differences. Formül: P^{s}_{j}(d) = f^{s}_{j}\big(d_{j}(A_{i},A_{l})\big) \in [0,1] Anchor: Diakoulaki-Koumoutsos 1991, p.5 Eq.(3)
4. 4.Adım 4 (F4): Step 4: Strong preference index π^s(A_i,A_l) = Σ w_j P^s_j(A_i,A_l). Formül: \pi^{s}(A_{i},A_{l}) = \sum_{j=1}^{n} P^{s}_{j}(A_{i},A_{l})\,w_{j} Anchor: Diakoulaki-Koumoutsos 1991, p.5 Eq.(4)
5. 5.Adım 5 (F5): Step 5: Combined flows φ^+(A_i) and φ^-(A_i) summing weak and strong preferences. Formül: \phi^{+}(A_{i}) = \dfrac{1}{m-1}\sum_{l\neq i}\big[\pi^{w}(A_{i},A_{l})+\pi^{s}(A_{i},A_{l})\big] Anchor: Diakoulaki-Koumoutsos 1991, p.6 Eq.(5)
6. 6.Adım 6 (F6): Step 6: Net flow φ(A_i) = φ^+(A_i) − φ^-(A_i). Formül: \phi(A_{i}) = \phi^{+}(A_{i}) - \phi^{-}(A_{i}) Anchor: Diakoulaki-Koumoutsos 1991, p.6 Eq.(6)
7. 7.Adım 7 (F7): Step 7: EXPROM I partial ranking from (φ^+, φ^-); EXPROM II full ranking from φ. Formül: \text{EXPROM I: partial};\quad \text{EXPROM II: rank by }\phi(A_{i})\text{ descending} Anchor: Diakoulaki-Koumoutsos 1991, p.6 Sec.4

Commonly paired with

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

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