IV-EDAS - EDAS yönteminin Aralık Değerli Sezgisel Bulanık uzantısı

Formül adımları

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

1. normalization

   $${\widehat{a}}_{ij}^c=([{\nu }^L,{\nu }^U],[{\mu }^L,{\mu }^U])(\text{cost});s_{ij}=\frac{{\mu }_{ij}^L+{\mu }_{ij}^U-{\nu }_{ij}^L-{\nu }_{ij}^U}{2}$$
   LaTeX

   \hat{a}_{ij}^c=([\nu^L,\nu^U],[\mu^L,\mu^U])\;(\text{cost});\quad s_{ij}=\frac{\mu^L_{ij}+\mu^U_{ij}-\nu^L_{ij}-\nu^U_{ij}}{2}

2. ranking_computation

   $$A{V}_j=\frac{1}{m}\sum _{i=1}^m{s}_{ij}$$
   LaTeX

   AV_j=\frac{1}{m}\sum_{i=1}^m s_{ij}

3. ranking_computation

   $$PD{A}_{ij}=\{\begin{array}{cc}{\displaystyle \frac{max(0,s_{ij}-A{V}_j)}{|A{V}_j|}}\hfill & j\in {\Omega }^{+}\hfill \\ [\mathrm{4pt}]{\displaystyle \frac{max(0,A{V}_j-s_{ij})}{|A{V}_j|}}\hfill & j\in {\Omega }^{-}\hfill \end{array}$$
   LaTeX

   PDA_{ij}=\begin{cases}\dfrac{\max(0,s_{ij}-AV_j)}{|AV_j|} & j\in\Omega^+\\[4pt]\dfrac{\max(0,AV_j-s_{ij})}{|AV_j|} & j\in\Omega^-\end{cases}

4. ranking_computation

   $$ND{A}_{ij}=\{\begin{array}{cc}{\displaystyle \frac{max(0,A{V}_j-s_{ij})}{|A{V}_j|}}\hfill & j\in {\Omega }^{+}\hfill \\ [\mathrm{4pt}]{\displaystyle \frac{max(0,s_{ij}-A{V}_j)}{|A{V}_j|}}\hfill & j\in {\Omega }^{-}\hfill \end{array}$$
   LaTeX

   NDA_{ij}=\begin{cases}\dfrac{\max(0,AV_j-s_{ij})}{|AV_j|} & j\in\Omega^+\\[4pt]\dfrac{\max(0,s_{ij}-AV_j)}{|AV_j|} & j\in\Omega^-\end{cases}

5. ranking_computation

   $$S{P}_i=\sum _{j=1}^n{w}_{j}PD{A}_{ij},S{N}_i=\sum _{j=1}^n{w}_{j}ND{A}_{ij}$$
   LaTeX

   SP_i=\sum_{j=1}^n w_j\,PDA_{ij},\quad SN_i=\sum_{j=1}^n w_j\,NDA_{ij}

6. ranking_computation

   $$NS{P}_i=\frac{S{P}_i}{{max}_{k}S{P}_k},NS{N}_i=1-\frac{S{N}_i}{{max}_{k}S{N}_k},A{S}_i=\frac{1}{2}(NS{P}_i+NS{N}_i),\text{rank descending}$$
   LaTeX

   NSP_i=\frac{SP_i}{\max_k SP_k},\quad NSN_i=1-\frac{SN_i}{\max_k SN_k},\quad AS_i=\tfrac{1}{2}(NSP_i+NSN_i),\quad\text{rank descending}

Sezgi

Sonucu okuma: iv-edas extends EDAS 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 EDAS 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.