FF-WPM - FF-WPM yönteminin Fermatean uzantısı

Formül adımları

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

1. Cost complement; apply FFWG.

   $$j\in {\Omega }_c:{\widehat{a}}_{ij}=({\nu }_{ij},{\mu }_{ij});{\mathrm{F}\mathrm{F}\mathrm{W}\mathrm{G}}_w({\alpha }_1,\dots ,{\alpha }_n)=(\prod _j{\mu }_j^{w_j},(1-\prod _j(1-{\nu }_j^3{)}^{w_j}{)}^{1/3});{\tilde{P}}_i={\mathrm{F}\mathrm{F}\mathrm{W}\mathrm{G}}_w({\widehat{a}}_{i1},\dots ,{\widehat{a}}_{in})$$
   LaTeX

   j\in\Omega_c:\;\hat{a}_{ij}=(\nu_{ij},\mu_{ij});\;\mathrm{FFWG}_w(\alpha_1,\ldots,\alpha_n)=\bigl(\prod_j\mu_j^{w_j},\;(1-\prod_j(1-\nu_j^3)^{w_j})^{1/3}\bigr);\;\tilde{P}_i=\mathrm{FFWG}_w(\hat{a}_{i1},\ldots,\hat{a}_{in})

2. Score s_i = μ³ - ν³; rank descending.

   $$s_i=({\tilde{\mu }}_i^P{)}^3-({\tilde{\nu }}_i^P{)}^3;\text{rank descending}$$
   LaTeX

   s_i=(\tilde{\mu}_i^P)^3-(\tilde{\nu}_i^P)^3;\quad\text{rank descending}

Sezgi

Sonucu okuma: ff-wpm extends FF-WPM 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 WPM 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.