Grey-WASPAS - WASPAS yönteminin Grey uzantısı

Formül adımları

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

1. Adım 1 — Gri normalleştirme ve beyazlatma.

   $${\widehat{v}}_{ij}=\frac{1}{2}(v_{ij}^{L,\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}+v_{ij}^{U,\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}})$$
   LaTeX

   \hat{v}_{ij}=\tfrac{1}{2}\bigl(v_{ij}^{L,\mathrm{norm}}+v_{ij}^{U,\mathrm{norm}}\bigr)

2. Adım 2 — Ağırlıklı toplam.

   $$Q_i^{(1)}=\sum _j{w}_j{\widehat{v}}_{ij}$$
   LaTeX

   Q_i^{(1)}=\sum_j w_j\hat{v}_{ij}

3. Adım 3 — Ağırlıklı çarpım.

   $$Q_i^{(2)}=\prod _j{\widehat{v}}_{ij}^{w_j}$$
   LaTeX

   Q_i^{(2)}=\prod_j\hat{v}_{ij}^{w_j}

4. Adım 4 — Birleşik skor ve azalan sıra.

   $$\begin{gathered} Q_i=\lambda Q_i^{(1)}+(1-\lambda )Q_i^{(2)},\lambda =0.5; \\ \text{rank descending} \end{gathered}$$
   LaTeX

   Q_i=\lambda Q_i^{(1)}+(1-\lambda)Q_i^{(2)},\quad\lambda=0.5;\\ \text{rank descending}

Sezgi

Grey outranking/ranking - Grey Interval Number (GIN: [x̲, x̄]). Output typically utility (higher value = preferred).

Sonucu okuma: grey-waspas extends WASPAS to handle Grey uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Grey Interval Number (GIN: [x̲, x̄]) algebra. The final scores are defuzzified via whitenisation: (x̲ + x̄)/2 before ranking.

Varsayımlar

• Decision matrix entries are valid Grey numbers/tuples
• Underlying crisp method's compensation assumption holds in uncertain space
• All decision-maker(s) and experts use the same linguistic/uncertainty scale

Ne zaman kullanılmaz

• Classical data sufficient - use base WASPAS directly (avoid unnecessary uncertainty layer)
• Aggregation operator (PFWA/PFOWA/etc.) not specified - output ambiguous

Sınırlılıklar

• Rank reversal known on alternative-set changes (ref: inherited from crisp base; cf. Belton-Gear 1983, Wang-Luo 2009)
• Assumes: Decision matrix entries are valid Grey numbers/tuples
• Assumes: Underlying crisp method's compensation assumption holds in uncertain space
• Assumes: All decision-maker(s) and experts use the same linguistic/uncertainty scale

Sık yapılan hatalar

• Değer-uzayı ihlali: hesaplamadan önce tüm girişlerin GIN: x̲ ≤ x̄ (lower and upper bounds of interval) koşulunu sağladığından emin olun.
• Defuzzifikasyon yöntemi sıralamayı etkiler: whitenisation: (x̲ + x̄)/2 kanonik seçimdir.