IV-ARAS - ARAS yönteminin Aralık Değerli Sezgisel Bulanık uzantısı

Formül adımları

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

1. normalization

   $${\widehat{a}}_{ij}^c=([{\nu }^L,{\nu }^U],[{\mu }^L,{\mu }^U])(\text{cost});A_0=([{max}_i{\mu }_{ij}^L,{max}_i{\mu }_{ij}^U],[{min}_i{\nu }_{ij}^L,{min}_i{\nu }_{ij}^U])$$
   LaTeX

   \hat{a}_{ij}^c=([\nu^L,\nu^U],[\mu^L,\mu^U])\;(\text{cost});\quad A_0=\bigl([\max_i\mu^L_{ij},\max_i\mu^U_{ij}],[\min_i\nu^L_{ij},\min_i\nu^U_{ij}]\bigr)

2. ranking_computation

   $${\tilde{v}}_{ij}=w_j\otimes {\widehat{a}}_{ij}=([1-(1-{\mu }_{ij}^L{)}^{w_j},1-(1-{\mu }_{ij}^U{)}^{w_j}],[{\nu }_{ij}^L{}^{w_j},{\nu }_{ij}^U{}^{w_j}])$$
   LaTeX

   \tilde{v}_{ij}=w_j\otimes\hat{a}_{ij}=\Bigl([1-(1-\mu^L_{ij})^{w_j},\;1-(1-\mu^U_{ij})^{w_j}],\;[\nu^L_{ij}{}^{w_j},\nu^U_{ij}{}^{w_j}]\Bigr)

3. 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)

4. ranking_computation

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

   s(\tilde{S}_i)=\frac{\mu^L_i+\mu^U_i-\nu^L_i-\nu^U_i}{2}

5. ranking_computation

   $$K_i=\frac{s({\tilde{S}}_i)}{s({\tilde{S}}_0)},\text{rank descending}$$
   LaTeX

   K_i=\frac{s(\tilde{S}_i)}{s(\tilde{S}_0)},\quad\text{rank descending}

Sezgi

Sonucu okuma: iv-aras extends ARAS 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 ARAS 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.