IF-SAW - SAW yönteminin Intuitionistic uzantısı

Formül adımları

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

1. normalization

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

   \tilde{a}_{ij}^c=(\nu_{ij},\mu_{ij})\quad\text{for cost criteria}

2. aggregation

   $${\tilde{S}}_i=\mathrm{I}\mathrm{F}\mathrm{W}\mathrm{A}(w,{\tilde{a}}_i)=(1-\prod _{j=1}^n(1-{\mu }_{ij}{)}^{w_j},\prod _{j=1}^n{\nu }_{ij}^{w_j})$$
   LaTeX

   \tilde{S}_i=\mathrm{IFWA}(w,\tilde{a}_i)=\Bigl(1-\prod_{j=1}^n(1-\mu_{ij})^{w_j},\;\prod_{j=1}^n\nu_{ij}^{w_j}\Bigr)

3. ranking_computation

   $$s({\tilde{S}}_i)={\mu }_i-{\nu }_i,\text{rank descending}$$
   LaTeX

   s(\tilde{S}_i)=\mu_i-\nu_i,\quad\text{rank descending}

Sezgi

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

Varsayımlar

• Decision matrix entries are valid Intuitionistic 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 IFN: μ ∈ [0,1], ν ∈ [0,1], μ+ν ≤ 1; π = 1−μ−ν ≥ 0 koşulunu sağladığından emin olun.
• Defuzzifikasyon yöntemi sıralamayı etkiler: score function S = μ − ν kanonik seçimdir.