WEBIRA - Ağırlıklı Çift Yönlü İdeal Oran Analizi

Formül adımları

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

1. Adım 1 — Her kriter için ideal x*_j ve anti-ideal x°_j belirle.

   $$x_j^{*}={max}_i{x}_{ij}\text{ (benefit)},{min}_i{x}_{ij}\text{ (cost)};x_j^{\circ }={min}_i{x}_{ij}\text{ (benefit)},{max}_i{x}_{ij}\text{ (cost)}$$
   LaTeX

   x_{j}^{*} = \max_{i}x_{ij} \text{ (benefit)},\;\min_{i}x_{ij} \text{ (cost)};\quad x_{j}^{\circ} = \min_{i}x_{ij} \text{ (benefit)},\;\max_{i}x_{ij} \text{ (cost)}

2. Adım 2 — Pozitif oran R⁺_ij (ideale yakınlık) ve negatif oran R⁻_ij (anti-ideale yakınlık) hesapla.

   $$R_{ij}^{+}=\frac{x_{ij}}{x_j^{*}},R_{ij}^{-}=\frac{x_j^{\circ }}{x_{ij}}$$
   LaTeX

   R_{ij}^{+} = \frac{x_{ij}}{x_{j}^{*}},\qquad R_{ij}^{-} = \frac{x_{j}^{\circ}}{x_{ij}}

3. Adım 3 — WEBIRA skoru B_i = (R⁺_ij − R⁻_ij)'nin ağırlıklı toplamı. Azalan sırada sırala.

   $$B_i=\sum _{j=1}^n{w}_j(R_{ij}^{+}-R_{ij}^{-})$$
   LaTeX

   B_{i} = \sum_{j=1}^{n}w_{j}\bigl(R_{ij}^{+} - R_{ij}^{-}\bigr)

Sezgi

Bidirectional ideal ratio scoring. Output typically utility (higher value = preferred).

Sonucu okuma: B_i can be any real number. Higher B means the alternative is closer to the ideal and farther from the anti-ideal, summed across all criteria weighted. B_i = 0 means equal proximity to ideal and anti-ideal on a weighted average.

Varsayımlar

• Criteria preferences are independent (no synergistic interactions)
• Compensation is acceptable: high score on one criterion can offset low on another
• Decision matrix is complete (no missing values)

Ne zaman kullanılmaz

• Criteria strongly correlated → consider DEMATEL/ANP for interdependence
• Non-compensatory preferences → consider outranking (ELECTRE/PROMETHEE)

Sınırlılıklar

• Assumes: Criteria preferences are independent (no synergistic interactions)
• Assumes: Compensation is acceptable: high score on one criterion can offset low on another
• Assumes: Decision matrix is complete (no missing values)

Sık yapılan hatalar

• Tüm alternatifler bir kriterinde özdeş: ideal = anti-ideal, R⁺ = R⁻ = 1, o kriter skora 0 katkı yapar - kabul edilebilir ancak dejenere sütunları kontrol edin.