IV-COPRAS - COPRAS yönteminin Aralık Değerli Sezgisel Bulanık uzantısı

Formül adımları

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

1. normalization

   $${\tilde{a}}_{ij}^c=([{\nu }_{ij}^L,{\nu }_{ij}^U],[{\mu }_{ij}^L,{\mu }_{ij}^U])\text{for cost criteria}$$
   LaTeX

   \tilde{a}_{ij}^c=([\nu^L_{ij},\nu^U_{ij}],[\mu^L_{ij},\mu^U_{ij}])\quad\text{for cost criteria}

2. ranking_computation

   $$s_{ij}=\frac{{\mu }_{ij}^L+{\mu }_{ij}^U-{\nu }_{ij}^L-{\nu }_{ij}^U}{2},{\widehat{s}}_{ij}=\frac{s_{ij}+1}{{\sum }_{i=1}^m(s_{ij}+1)},v_{ij}=w_j{\widehat{s}}_{ij}$$
   LaTeX

   s_{ij}=\frac{\mu^L_{ij}+\mu^U_{ij}-\nu^L_{ij}-\nu^U_{ij}}{2},\quad\hat{s}_{ij}=\frac{s_{ij}+1}{\sum_{i=1}^m(s_{ij}+1)},\quad v_{ij}=w_j\hat{s}_{ij}

3. ranking_computation

   $$S_i^{+}=\sum _{j\in {\Omega }^{+}}{v}_{ij},S_i^{-}=\sum _{j\in {\Omega }^{-}}{v}_{ij}$$
   LaTeX

   S_i^+=\sum_{j\in\Omega^+}v_{ij},\quad S_i^-=\sum_{j\in\Omega^-}v_{ij}

4. ranking_computation

   $$Q_i=S_i^{+}+\frac{S_{min}^{-}{\sum }_{i=1}^m{S}_i^{-}}{S_i^{-}{\sum }_{i=1}^m\frac{S_{min}^{-}}{S_i^{-}}}$$
   LaTeX

   Q_i=S_i^++\frac{S_{\min}^-\sum_{i=1}^m S_i^-}{S_i^-\sum_{i=1}^m\frac{S_{\min}^-}{S_i^-}}

5. ranking_computation

   $$N_i=\frac{Q_i}{Q_{max}}\times 100\%,\text{rank descending}$$
   LaTeX

   N_i=\frac{Q_i}{Q_{\max}}\times100\%,\quad\text{rank descending}

Sezgi

Sonucu okuma: iv-copras extends COPRAS to handle Interval uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Interval Number (IN: [a, b]) algebra. The final scores are defuzzified via midpoint (a+b)/2 before ranking.

Varsayımlar

• Decision matrix entries are valid Interval 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 COPRAS directly (avoid unnecessary uncertainty layer)
• Aggregation operator (PFWA/PFOWA/etc.) not specified - output ambiguous

Sık yapılan hatalar

• Değer-uzayı ihlali: hesaplamadan önce tüm girişlerin IN: a ≤ b koşulunu sağladığından emin olun.
• Defuzzifikasyon yöntemi sıralamayı etkiler: midpoint (a+b)/2 kanonik seçimdir.