MOORA: Multi-Objective Optimisation by Ratio Analysis

Overview

Ratio system + reference point (vector normalisation). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Ratio system + reference point (vector normalisation)

Limitations

• •Rank reversal known on alternative-set changes (ref: general MCDM literature)
• •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 MOORA-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

• •Hatalı: 'MOORA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'MOORA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'MOORA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: MOORA'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: MOORA'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 = x_ij / √(Σ x_ij²). Formül: r_{ij} = \dfrac{x_{ij}}{\sqrt{\sum_{i=1}^{m} x_{ij}^{2}}} Anchor: Brauers-Zavadskas 2006, p.453 Eq.(2)
2. 2.Adım 2 (F2): Step 2: Weighted normalised matrix v_ij = w_j · r_ij. Formül: v_{ij} = w_{j}\,r_{ij} Anchor: Brauers-Zavadskas 2006, p.453 Eq.(3)
3. 3.Adım 3 (F3): Step 3: Ratio system y_i = Σ_{j∈J+} v_ij − Σ_{j∈J−} v_ij. Formül: y_{i} = \sum_{j\in J^{+}} v_{ij} - \sum_{j\in J^{-}} v_{ij} Anchor: Brauers-Zavadskas 2006, p.453 Eq.(4)
4. 4.Adım 4 (F4): Step 4: Descending ranking by y_i. Formül: \text{Rank descending: } y_{(1)}\ge y_{(2)}\ge\cdots\ge y_{(m)} Anchor: Brauers-Zavadskas 2006, p.453

Commonly paired with

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

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