MULTIMOORA: Multi-Objective Optimisation by Ratio Analysis plus Full Multiplicative Form

Overview

Dominance aggregation of three sub-rankings (RS + RP + FMF). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Dominance aggregation of three sub-rankings (RS + RP + FMF)

Limitations

• •Assumes: Criteria preferences are independent (no synergistic interactions)
• •Assumes: Compensation is acceptable: high score on one criterion can offset low on another
• •Assumes: Decision matrix is complete (no missing values)

Assumptions to verify

• •Criteria preferences are independent (no synergistic interactions)
• •Compensation is acceptable: high score on one criterion can offset low on another
• •Decision matrix is complete (no missing values)

When not to use

• •Criteria strongly correlated → consider DEMATEL/ANP for interdependence
• •Non-compensatory preferences → consider outranking (ELECTRE/PROMETHEE)

Edge cases

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

Common pitfalls

• •Hatalı: 'MULTIMOORA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'MULTIMOORA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'MULTIMOORA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: MULTIMOORA'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: MULTIMOORA'yi 'Non-compensatory preferences → consider outranking (ELECTRE/PROMETHEE)' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Vector normalisation r_ij. Formül: r_{ij} = \dfrac{x_{ij}}{\sqrt{\sum_{k=1}^{m} x_{kj}^{2}}} Anchor: Brauers-Zavadskas 2010, p.7 Eq.(2)
2. 2.Adım 2 (F2): Step 2: Ratio System y_i = Σ benefit − Σ cost. Formül: y_{i} = \sum_{j\in J^{+}} w_{j} r_{ij} - \sum_{j\in J^{-}} w_{j} r_{ij} Anchor: Brauers-Zavadskas 2010, p.7 Eq.(3)
3. 3.Adım 3 (F3): Step 3: Reference Point z_i = max(|w_j r_j* − w_j r_ij|). Formül: z_{i} = \max_{j} \Big|w_{j} r^{*}_{j} - w_{j} r_{ij}\Big|,\quad r^{*}_{j}=\max_{i} r_{ij}\ (J^{+})\ \text{or}\ \min_{i} r_{ij}\ (J^{-}) Anchor: Brauers-Zavadskas 2010, p.8 Eq.(5)
4. 4.Adım 4 (F4): Step 4: Full Multiplicative Form U_i = Π benefit / Π cost. Formül: U_{i} = \dfrac{\prod_{j\in J^{+}} (x_{ij})^{w_{j}}}{\prod_{j\in J^{-}} (x_{ij})^{w_{j}}} Anchor: Brauers-Zavadskas 2010, p.8 Eq.(7)
5. 5.Adım 5 (F5): Step 5: Dominance theory aggregation of three rankings. Formül: \text{Final rank} = \text{dominance}(\text{rank}(y_{i}),\,\text{rank}(z_{i}),\,\text{rank}(U_{i})) Anchor: Brauers-Zavadskas 2010, p.9

Commonly paired with

• •AHP + MULTIMOORA (high)
• •BWM + MULTIMOORA (high)
• •ENTROPY + MULTIMOORA (high)
• •CRITIC + MULTIMOORA (high)
• •SWARA + MULTIMOORA (high)

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