Hellwig Yöntemi - Gelişim Deseni

Formül adımları

Analiz motorunun yöntem bildirimindeki (manifest F.steps) adımlar; raporlardaki formüllerle aynı kaynaktır.

1. Adım 1 — Standartlaştırma z_ij.

   $$z_{ij}={\displaystyle \frac{x_{ij}-{\mu }_j}{{\sigma }_j}}$$
   LaTeX

   z_{ij} = \dfrac{x_{ij}-\mu_{j}}{\sigma_{j}}

2. Adım 2 — Referans örüntü z_0.

   $$z_{0j}={max}_i{z}_{ij}(J^{+})\text{or}{min}_i{z}_{ij}(J^{-})$$
   LaTeX

   z_{0j}=\max_{i} z_{ij}\ (J^{+})\ \text{or}\ \min_{i} z_{ij}\ (J^{-})

3. Adım 3 — Referanstan Öklid uzaklığı.

   $$d_{i0}=\sqrt{{\sum }_{j=1}^n(z_{ij}-z_{0j}{)}^2}$$
   LaTeX

   d_{i0} = \sqrt{\sum_{j=1}^{n}(z_{ij}-z_{0j})^{2}}

4. Adım 4 — Hellwig ölçüsü h_i.

   $$h_i=1-{\displaystyle \frac{d_{i0}}{d_0}},d_0=\overline{d}+2{\sigma }_d$$
   LaTeX

   h_{i} = 1 - \dfrac{d_{i0}}{d_{0}},\quad d_{0} = \bar{d} + 2\sigma_{d}

Sezgi

Taxonomic distance-from-ideal (development measure). Output typically utility (higher value = preferred).

Sonucu okuma: m_i ∈ (−∞,1]. Higher m means closer to the ideal pattern. m_i close to 1 = excellent development level. m_i < 0 means the alternative is farther from ideal than the critical distance d⁰. Hellwig's method is weight-free by design - all criteria are treated equally. It is widely used in regional/country development studies.

Varsayımlar

• 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)

Ne zaman kullanılmaz

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

Sınırlılıklar

• 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)

Sık yapılan hatalar

• Sabit sütun: standart sapma = 0, z-skor tanımsız - E-2'yi kontrol edin.