MAIRCA: Multi-Attributive Ideal-Real Comparative Analysis

Overview

Gap matrix (theoretical vs actual preference). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Gap matrix (theoretical vs actual preference)

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

Common pitfalls

• •Hatalı: 'MAIRCA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'MAIRCA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'MAIRCA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: MAIRCA'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: MAIRCA'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: Define theoretical preference T_Aij: uniform probability that each alternative is chosen = 1/m. Multiply by weights. Formül: T_{Aij} = w_{j}\cdot\frac{1}{m} Anchor: Pamučar et al. 2014, p.90 Eq.(1)
2. 2.Adım 2 (F2): Step 2: Normalise decision matrix using linear normalisation. Formül: n_{ij} = \frac{x_{ij}-\min_{k}x_{kj}}{\max_{k}x_{kj}-\min_{k}x_{kj}} \text{ (benefit)};\quad n_{ij} = \frac{\max_{k}x_{kj}-x_{ij}}{\max_{k}x_{kj}-\min_{k}x_{kj}} \text{ (cost)} Anchor: Pamučar et al. 2014, p.90 Eq.(2)
3. 3.Adım 3 (F3): Step 3: Compute actual preference R_Aij = T_Aij × n_ij. Formül: R_{Aij} = T_{Aij}\cdot n_{ij} Anchor: Pamučar et al. 2014, p.90 Eq.(3)
4. 4.Adım 4 (F4): Step 4: Compute total gap G_ij = T_Aij - R_Aij and total gap per alternative Q_i. Rank in ascending order (lower gap = better). Formül: G_{ij} = T_{Aij} - R_{Aij};\qquad Q_{i} = \sum_{j=1}^{n} G_{ij} Anchor: Pamučar et al. 2014, p.91 Eqs.(4)-(5)

Commonly paired with

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

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