HF-SAW - HF-SAW yönteminin Hesitant uzantısı

Formül adımları

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

1. ranking_computation

   $$h^{\sigma }=h\cup \{{min}_{\gamma \in h}\gamma {\}}^{(l_{max}-l)},h^c=\{1-\gamma \mid \gamma \in h\}\text{(cost)}$$
   LaTeX

   h^{\sigma}=h\cup\{\min_{\gamma\in h}\gamma\}^{(l_{\max}-l)},\quad h^{c}=\{1-\gamma\mid\gamma\in h\}\;\text{(cost)}

2. aggregation

   $${\tilde{h}}_i={⨁}_{j=1}^n{w}_j{h}_{ij}=\backslash \{1-\prod _{j=1}^n(1-{\gamma }_j{)}^{w_j}|{\gamma }_j\in h_{ij}\backslash \}$$
   LaTeX

   \tilde{h}_i=\bigoplus_{j=1}^n w_j h_{ij}=\Bigl\{1-\prod_{j=1}^n(1-\gamma_j)^{w_j}\;\Big|\;\gamma_j\in h_{ij}\Bigr\}

3. ranking_computation

   $$s({\tilde{h}}_i)=\frac{1}{l}\sum _{k=1}^l{\gamma }^{(k)},\text{rank descending}$$
   LaTeX

   s(\tilde{h}_i)=\frac{1}{l}\sum_{k=1}^{l}\gamma^{(k)},\quad\text{rank descending}

Sezgi

Sonucu okuma: hf-saw extends HF-SAW 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 SAW 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.