COCOSO - Birleşik Uzlaşı Çözümü

Formül adımları

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

1. Adım 1 — Kriter türüne göre uzlaşı normalleştirmesi.

   $$r_{ij}=\{\begin{array}{cc}{\displaystyle \frac{x_{ij}-min{x}_{ij}}{max{x}_{ij}-min{x}_{ij}}}\hfill & j\in J^{+}\hfill \\ {\displaystyle \frac{max{x}_{ij}-x_{ij}}{max{x}_{ij}-min{x}_{ij}}}\hfill & j\in J^{-}\hfill \end{array}$$
   LaTeX

   r_{ij} = \begin{cases} \dfrac{x_{ij}-\min x_{ij}}{\max x_{ij}-\min x_{ij}} & j\in J^{+} \\ \dfrac{\max x_{ij}-x_{ij}}{\max x_{ij}-\min x_{ij}} & j\in J^{-} \end{cases}

2. Adım 2 — Ağırlıklı toplam bileşeni S_i.

   $$S_i=\sum _{j=1}^n{w}_j{r}_{ij}$$
   LaTeX

   S_{i} = \sum_{j=1}^{n} w_{j}\,r_{ij}

3. Adım 3 — Ağırlıklı çarpım bileşeni P_i.

   $$P_i=\sum _{j=1}^n(r_{ij}{)}^{w_j}$$
   LaTeX

   P_{i} = \sum_{j=1}^{n} (r_{ij})^{w_{j}}

4. Adım 4 — Üç değerlendirme skoru k_a, k_b, k_c.

   $$k_{a,i}={\displaystyle \frac{P_i+S_i}{{\sum }_k(P_k+S_k)}},k_{b,i}={\displaystyle \frac{S_i}{{min}_k{S}_k}}+{\displaystyle \frac{P_i}{{min}_k{P}_k}},k_{c,i}={\displaystyle \frac{\lambda S_i+(1-\lambda )P_i}{\lambda {max}_k{S}_k+(1-\lambda ){max}_k{P}_k}}$$
   LaTeX

   k_{a,i}=\dfrac{P_{i}+S_{i}}{\sum_{k}(P_{k}+S_{k})},\ \ k_{b,i}=\dfrac{S_{i}}{\min_{k} S_{k}}+\dfrac{P_{i}}{\min_{k} P_{k}},\ \ k_{c,i}=\dfrac{\lambda S_{i}+(1-\lambda)P_{i}}{\lambda \max_{k} S_{k}+(1-\lambda)\max_{k} P_{k}}

5. Adım 5 — Nihai uzlaşı k_i ve azalan sıralama.

   $$k_i=(k_{a,i}{k}_{b,i}{k}_{c,i}{)}^{1/3}+\frac{1}{3}(k_{a,i}+k_{b,i}+k_{c,i})$$
   LaTeX

   k_{i} = (k_{a,i}\,k_{b,i}\,k_{c,i})^{1/3} + \tfrac{1}{3}(k_{a,i}+k_{b,i}+k_{c,i})

Sezgi

Aggregated exponential comparison (WSM + WPM combination). Output typically utility (higher value = preferred).

Sonucu okuma: k_i > 0. Higher k_i means better. COCOSO combines three appraisal strategies (k_ia: proportional total, k_ib: ratio to minimum, k_ic: weighted λ-compromise) into a geometric-arithmetic mean. The three strategies check robustness - if all three agree, the ranking is stable.

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

• Sabit kriter sütunu: min-maks normalleştirme paydası sıfırdır - E-2'yi kontrol edin.