FF-EDAS - FF-EDAS yönteminin Fermatean uzantısı

Formül adımları

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

1. FF scores s_ij = μ³ - ν³.

   $$s_{ij}={\mu }_{ij}^3-{\nu }_{ij}^3$$
   LaTeX

   s_{ij}=\mu_{ij}^3-\nu_{ij}^3

2. Average score per criterion.

   $${\overline{s}}_j=\frac{1}{m}\sum _i{s}_{ij}$$
   LaTeX

   \bar{s}_j=\tfrac{1}{m}\sum_i s_{ij}

3. PDA and NDA from average.

   $${\mathrm{P}\mathrm{D}\mathrm{A}}_{ij}=max(0,s_{ij}-{\overline{s}}_j)/|{\overline{s}}_j|(j\in {\Omega }_b);{\mathrm{N}\mathrm{D}\mathrm{A}}_{ij}=max(0,{\overline{s}}_j-s_{ij})/|{\overline{s}}_j|;\text{swapped for cost}$$
   LaTeX

   \mathrm{PDA}_{ij}=\max(0,s_{ij}-\bar{s}_j)/|\bar{s}_j|\;(j\in\Omega_b);\;\mathrm{NDA}_{ij}=\max(0,\bar{s}_j-s_{ij})/|\bar{s}_j|;\;\text{swapped for cost}

4. SP_i, SN_i; normalise.

   $$S{P}_i=\sum _j{w}_j{\mathrm{P}\mathrm{D}\mathrm{A}}_{ij};S{N}_i=\sum _j{w}_j{\mathrm{N}\mathrm{D}\mathrm{A}}_{ij};NS{P}_i=S{P}_i/maxSP;NS{N}_i=1-S{N}_i/maxSN$$
   LaTeX

   SP_i=\sum_j w_j\mathrm{PDA}_{ij};\;SN_i=\sum_j w_j\mathrm{NDA}_{ij};\;NSP_i=SP_i/\max SP;\;NSN_i=1-SN_i/\max SN

5. Appraisal score; rank descending.

   $$A{S}_i=(NS{P}_i+NS{N}_i)/2;\text{rank descending}$$
   LaTeX

   AS_i=(NSP_i+NSN_i)/2;\quad\text{rank descending}

6. Final ranking output.

   $$A_{\sigma (1)}\succ \cdots \succ A_{\sigma (m)}$$
   LaTeX

   A_{\sigma(1)}\succ\cdots\succ A_{\sigma(m)}

Sezgi

Sonucu okuma: ff-edas extends FF-EDAS to handle Fermatean uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Fermatean Fuzzy Set (FFS: μ, ν; μ³+ν³ ≤ 1) algebra. The final scores are defuzzified via score function S = μ³ − ν³ before ranking.

Varsayımlar

• Decision matrix entries are valid Fermatean 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 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 FFS: μ³+ν³ ≤ 1 (q=3 special case of q-ROF) koşulunu sağladığından emin olun.
• Defuzzifikasyon yöntemi sıralamayı etkiler: score function S = μ³ − ν³ kanonik seçimdir.