HF-CODAS - HF-CODAS yönteminin Hesitant uzantısı

Formül adımları

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

1. ranking_computation

   $$h^{\sigma }=h\cup \{{min}_{\gamma \in h}\gamma {\}}^{(l_{max}-l)}\text{pad to length }{l}_{max}$$
   LaTeX

   h^{\sigma}=h\cup\{\min_{\gamma\in h}\gamma\}^{(l_{\max}-l)}\quad\text{pad to length }l_{\max}

2. normalisation

   $$h_{ij}^N=\{\begin{array}{cc}{h}_{ij}\hfill & \text{benefit}\hfill \\ 1-h_{ij}\hfill & \text{cost}\hfill \end{array},{\overline{h}}_{ij}=w_j\otimes h_{ij}^N=\{1-(1-\gamma {)}^{w_j}\mid \gamma \in h_{ij}^N\}$$
   LaTeX

   h_{ij}^{N}=\begin{cases}h_{ij} & \text{benefit}\\1-h_{ij} & \text{cost}\end{cases},\quad\bar{h}_{ij}=w_j\otimes h_{ij}^{N}=\{1-(1-\gamma)^{w_j}\mid\gamma\in h_{ij}^{N}\}

3. ranking_computation

   $$h_j^{-}={min}_{i}s(h_{ij}),s(h)=\frac{1}{l}\sum _{k=1}^l{\gamma }^{(k)}$$
   LaTeX

   h_j^{-}=\min_i s(h_{ij}),\quad s(h)=\frac{1}{l}\sum_{k=1}^{l}\gamma^{(k)}

4. ranking_computation

   $$E_i=\sqrt{{\sum }_{j=1}^n[s({\overline{h}}_{ij})-s(h_j^{-}){]}^2},T_i=\sum _{j=1}^n|s({\overline{h}}_{ij})-s(h_j^{-})|$$
   LaTeX

   E_i=\sqrt{\sum_{j=1}^n\bigl[s(\bar{h}_{ij})-s(h_j^{-})\bigr]^2},\quad T_i=\sum_{j=1}^n\bigl|s(\bar{h}_{ij})-s(h_j^{-})\bigr|

5. ranking_computation

   $$h_{ik}=(E_i-E_k)+\psi (E_i-E_k)(T_i-T_k),\psi (x)=\{\begin{array}{cc}1\hfill & |x|\ge \tau \hfill \\ 0\hfill & |x|<\tau \hfill \end{array},\tau =0.02$$
   LaTeX

   h_{ik}=(E_i-E_k)+\psi(E_i-E_k)(T_i-T_k),\quad\psi(x)=\begin{cases}1&|x|\geq\tau\\0&|x|<\tau\end{cases},\;\tau=0.02

6. ranking_computation

   $$A{S}_i=\sum _{k=1}^m{h}_{ik},\text{rank descending}$$
   LaTeX

   AS_i=\sum_{k=1}^m h_{ik},\quad\text{rank descending}

Sezgi

Sonucu okuma: hf-codas extends HF-CODAS to handle Hesitant uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Hesitant Fuzzy Element (HFE: set of possible membership degrees) algebra. The final scores are defuzzified via envelope: (min + max)/2, or mean of all values before ranking.

Varsayımlar

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

Sık yapılan hatalar

• Değer-uzayı ihlali: hesaplamadan önce tüm girişlerin HFE: non-empty finite set of values in [0,1] koşulunu sağladığından emin olun.
• Defuzzifikasyon yöntemi sıralamayı etkiler: envelope: (min + max)/2, or mean of all values kanonik seçimdir.