IV-SAW - SAW yönteminin Aralık Değerli Sezgisel Bulanık uzantısı

Formül adımları

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

1. normalization

   $${\tilde{a}}_{ij}^c=([{\nu }_{ij}^L,{\nu }_{ij}^U],[{\mu }_{ij}^L,{\mu }_{ij}^U])\text{for cost criteria}$$
   LaTeX

   \tilde{a}_{ij}^c=([\nu^L_{ij},\nu^U_{ij}],[\mu^L_{ij},\mu^U_{ij}])\quad\text{for cost criteria}

2. aggregation

   $${\tilde{S}}_i=\mathrm{I}\mathrm{I}\mathrm{F}\mathrm{W}\mathrm{A}(w,{\widehat{a}}_i)=([1-\prod _j(1-{\mu }_{ij}^L{)}^{w_j},1-\prod _j(1-{\mu }_{ij}^U{)}^{w_j}],[\prod _j{\nu }_{ij}^L{}^{w_j},\prod _j{\nu }_{ij}^U{}^{w_j}])$$
   LaTeX

   \tilde{S}_i=\mathrm{IIFWA}(w,\hat{a}_i)=\Bigl([1-\textstyle\prod_j(1-\mu^L_{ij})^{w_j},\;1-\textstyle\prod_j(1-\mu^U_{ij})^{w_j}],\;[\textstyle\prod_j\nu^L_{ij}{}^{w_j},\textstyle\prod_j\nu^U_{ij}{}^{w_j}]\Bigr)

3. ranking_computation

   $$s({\tilde{S}}_i)=\frac{{\mu }_i^L+{\mu }_i^U-{\nu }_i^L-{\nu }_i^U}{2},\text{rank descending}$$
   LaTeX

   s(\tilde{S}_i)=\frac{\mu^L_i+\mu^U_i-\nu^L_i-\nu^U_i}{2},\quad\text{rank descending}

Sezgi

Sonucu okuma: iv-saw extends SAW to handle Interval uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Interval Number (IN: [a, b]) algebra. The final scores are defuzzified via midpoint (a+b)/2 before ranking.

Varsayımlar

• Decision matrix entries are valid Interval 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 IN: a ≤ b koşulunu sağladığından emin olun.
• Defuzzifikasyon yöntemi sıralamayı etkiler: midpoint (a+b)/2 kanonik seçimdir.