DNMA: Double Normalization-Based Multiple Aggregation

Overview

Dual-normalisation aggregation (linear + vector). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Dual-normalisation aggregation (linear + vector)

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

• •ties: complete (WSM), incomplete (WPM), and TOPSIS-like.

Common pitfalls

• •Hatalı: 'DNMA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'DNMA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'DNMA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: DNMA'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: DNMA'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: Three normalisations: linear-max, vector, and target-based. Formül: r^{(1)}_{ij}=\dfrac{x_{ij}}{\max x_{ij}};\ r^{(2)}_{ij}=\dfrac{x_{ij}}{\sqrt{\sum x_{kj}^{2}}};\ r^{(3)}_{ij}\text{ target-based} Anchor: Liao-Wu 2020, p.6 Eqs.(1)-(3)
2. 2.Adım 2 (F2): Step 2: Three sub-utilities: complete (WSM), incomplete (WPM), and TOPSIS-like. Formül: u^{(1)}_{i}=\sum w_{j} r^{(1)}_{ij},\ u^{(2)}_{i}=\prod r^{(2)\,w_{j}}_{ij},\ u^{(3)}_{i}=\text{TOPSIS closeness} Anchor: Liao-Wu 2020, p.7 Eqs.(4)-(6)
3. 3.Adım 3 (F3): Step 3: Compute three ranks R^{(k)}_i; deviation measure considers rank spread. Formül: R^{(k)}_{i}=\text{rank}(u^{(k)}_{i});\ S^{(k)}_{i}=u^{(k)}_{i}-\min_{l} u^{(k)}_{l} Anchor: Liao-Wu 2020, p.8 Eq.(7)
4. 4.Adım 4 (F4): Step 4: Combined DNMA score D_i = Σ α_k (u^{(k)}_i)^2 − Σ β_k (R^{(k)}_i)^2; descending ranking. Formül: D_{i} = \sum_{k=1}^{3} \alpha_{k}\,(u^{(k)}_{i})^{2} - \sum_{k=1}^{3} \beta_{k}\,(R^{(k)}_{i})^{2} Anchor: Liao-Wu 2020, p.8 Eq.(8)

Commonly paired with

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

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