NMD - Nesnel Kriter Ağırlıklarının Yeni Belirleme Yöntemi

Formül adımları

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

1. Adım 1 — Doğrusal-maks normalleştirme uygula.

   $$n_{ij}=x_{ij}/x_j^{max}\text{(benefit)};n_{ij}=x_j^{min}/x_{ij}\text{(cost)}$$
   LaTeX

   n_{ij}=x_{ij}/x_j^{\max}\text{(benefit)};\;n_{ij}=x_j^{\min}/x_{ij}\text{(cost)}

2. Adım 2 — Normalleştirilmiş matrisin sütun ortalaması μ_j hesapla. w_j = (1 − μ_j) / Σ_k (1 − μ_k).

   $${\mu }_j=\frac{1}{m}\sum _i{n}_{ij};w_j=\frac{1-{\mu }_j}{{\sum }_k(1-{\mu }_k)}$$
   LaTeX

   \mu_j=\frac{1}{m}\sum_i n_{ij};\quad w_j=\frac{1-\mu_j}{\sum_k(1-\mu_k)}

Sezgi

Weight_Objective (normalised matrix column-mean based). Output typically weight (higher value = preferred).

Sonucu okuma: NMD assigns higher weight to criteria whose alternatives perform further below the maximum (lower μ_j → more spread from the ideal). It is fully objective and simple to compute. Criteria where all alternatives score near 1 (all close to best) get low weight.

Varsayımlar

• Decision matrix exists with measurable criteria
• Sufficient inter-alternative variation per criterion

Ne zaman kullanılmaz

• No data variation (constant criterion) → weight degenerates
• Expert judgment is the actual driver → use subjective weighting

Sınırlılıklar

• Assumes: Decision matrix exists with measurable criteria
• Assumes: Sufficient inter-alternative variation per criterion

Sık yapılan hatalar

• μ_j = 1 ise (tüm alternatifler en iyi), w_j=0. Kriter bilgi vermez.