PF-WASPAS - WASPAS yönteminin Pythagorean uzantısı

Formül adımları

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

1. Cost complement.

   $$j\in {\Omega }_c:{\widehat{\alpha }}_{ij}=({\nu }_{ij},{\mu }_{ij})$$
   LaTeX

   j\in\Omega_c:\;\hat{\alpha}_{ij}=(\nu_{ij},\mu_{ij})

2. WSM via PFWA; WPM via PFWG.

   $$Q_i^{(1)}=s({\mathrm{P}\mathrm{F}\mathrm{W}\mathrm{A}}_w({\widehat{\alpha }}_{i1},\dots ,{\widehat{\alpha }}_{in}));Q_i^{(2)}=s({\mathrm{P}\mathrm{F}\mathrm{W}\mathrm{G}}_w({\widehat{\alpha }}_{i1},\dots ,{\widehat{\alpha }}_{in}))$$
   LaTeX

   Q_i^{(1)}=s(\mathrm{PFWA}_w(\hat{\alpha}_{i1},\ldots,\hat{\alpha}_{in}));\;Q_i^{(2)}=s(\mathrm{PFWG}_w(\hat{\alpha}_{i1},\ldots,\hat{\alpha}_{in}))

3. Combined Q_i; rank descending.

   $$Q_i=\lambda Q_i^{(1)}+(1-\lambda )Q_i^{(2)},\lambda =0.5;\text{rank descending}$$
   LaTeX

   Q_i=\lambda Q_i^{(1)}+(1-\lambda)Q_i^{(2)},\;\lambda=0.5;\quad\text{rank descending}

Sezgi

Sonucu okuma: pf-waspas extends WASPAS 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 WASPAS 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.