IF-COPRAS - COPRAS yönteminin Intuitionistic uzantısı

Formül adımları

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

1. ranking_computation

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

   s_{ij}=\mu_{ij}-\nu_{ij},\quad\hat{s}_{ij}=\frac{s_{ij}+1}{\sum_{i=1}^m(s_{ij}+1)},\quad v_{ij}=w_j\hat{s}_{ij}

2. 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}

3. 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^-}}

4. 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: if-copras extends COPRAS to handle Intuitionistic uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Intuitionistic Fuzzy Number (IFN: μ, ν; μ+ν ≤ 1) algebra. The final scores are defuzzified via score function S = μ − ν before ranking.

Varsayımlar

• Decision matrix entries are valid Intuitionistic Fuzzy 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 IFN: μ ∈ [0,1], ν ∈ [0,1], μ+ν ≤ 1; π = 1−μ−ν ≥ 0 koşulunu sağladığından emin olun.
• Defuzzifikasyon yöntemi sıralamayı etkiler: score function S = μ − ν kanonik seçimdir.