PF-SAW - SAW yönteminin Pythagorean uzantısı

Formül adımları

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

1. Cost complement; PFWA aggregate.

   $$j\in {\Omega }_c:{\widehat{\alpha }}_{ij}=({\nu }_{ij},{\mu }_{ij});{\mathrm{P}\mathrm{F}\mathrm{W}\mathrm{A}}_w({\alpha }_1,\dots ,{\alpha }_n)=((1-\prod _j(1-{\mu }_j^2{)}^{w_j}{)}^{1/2},\prod _j{\nu }_j^{w_j});{\tilde{Z}}_i={\mathrm{P}\mathrm{F}\mathrm{W}\mathrm{A}}_w({\widehat{\alpha }}_{i1},\dots ,{\widehat{\alpha }}_{in})$$
   LaTeX

   j\in\Omega_c:\;\hat{\alpha}_{ij}=(\nu_{ij},\mu_{ij});\;\mathrm{PFWA}_w(\alpha_1,\ldots,\alpha_n)=\bigl((1-\prod_j(1-\mu_j^2)^{w_j})^{1/2},\;\prod_j\nu_j^{w_j}\bigr);\;\tilde{Z}_i=\mathrm{PFWA}_w(\hat{\alpha}_{i1},\ldots,\hat{\alpha}_{in})

2. Score s_i = μ² - ν²; rank descending.

   $$s_i={\tilde{\mu }}_i^{Z2}-{\tilde{\nu }}_i^{Z2};\text{rank descending}$$
   LaTeX

   s_i=\tilde{\mu}_i^{Z2}-\tilde{\nu}_i^{Z2};\quad\text{rank descending}

Sezgi

Sonucu okuma: pf-saw extends SAW to handle Pythagorean uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Pythagorean Fuzzy Number (PFN: μ, ν; μ²+ν² ≤ 1) algebra. The final scores are defuzzified via score function S = μ² − ν² before ranking.

Varsayımlar

• Decision matrix entries are valid Pythagorean 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 PFN: μ ∈ [0,1], ν ∈ [0,1], μ²+ν² ≤ 1 koşulunu sağladığından emin olun.
• Defuzzifikasyon yöntemi sıralamayı etkiler: score function S = μ² − ν² kanonik seçimdir.