SIWEC - Basit Ağırlık Hesaplama

Formül adımları

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

1. Steps 1–2: each of the k decision makers grades all n criteria on a numerical scale (e.g. 1–10); a higher grade means a more important criterion. The grades form a k×n matrix (rows = decision makers, columns = criteria). No ranking or pairwise comparison is needed.

   $$X=[x_{ij}{]}_{k\times n};x_{ij}\in (0,\infty )$$
   LaTeX

   X = [x_{ij}]_{k×n}; x_{ij} \in (0,\infty)

2. Step 3: divide every grade by the largest grade in the whole matrix (all criteria, all decision makers) — not by a per-expert or per-criterion maximum. The paper chooses this on purpose: a decision maker who gives low grades keeps a low profile and low-rated criteria are not lifted to the level of high-rated ones.

   $$n_{ij}=\frac{x_{ij}}{x^{max}},x^{max}={max}_{i,j}{x}_{ij}$$
   LaTeX

   n_{ij} = \frac{x_{ij}}{x^{\max}},\quad x^{\max} = \max_{i,j} x_{ij}

3. Step 4: sample standard deviation of each decision maker's normalised grades (divisor n − 1; this reproduces the st.dev column of the paper's Table 3). A decision maker whose grades are more diverse gets more influence.

   $${\mathrm{s}\mathrm{t}.\mathrm{d}\mathrm{e}\mathrm{v}}_i=\sqrt{\frac{1}{n-1}{\sum }_{j=1}^n(n_{ij}-{\overline{n}}_i{)}^2};{\overline{n}}_i=\frac{1}{n}\sum _{j=1}^n{n}_{ij}$$
   LaTeX

   \mathrm{st.dev}_i = \sqrt{\frac{1}{n-1}\sum_{j=1}^{n}(n_{ij} - \bar{n}_i)^2};\quad \bar{n}_i = \frac{1}{n}\sum_{j=1}^{n} n_{ij}

4. Step 5: multiply each normalised grade by its decision maker's standard deviation.

   $$v_{ij}=n_{ij}\times {\mathrm{s}\mathrm{t}.\mathrm{d}\mathrm{e}\mathrm{v}}_i$$
   LaTeX

   v_{ij} = n_{ij} \times \mathrm{st.dev}_i

5. Step 6: sum the products over all decision makers for each criterion.

   $$s_j=\sum _{i=1}^k{v}_{ij}$$
   LaTeX

   s_j = \sum_{i=1}^{k} v_{ij}

6. Step 7: divide each criterion sum by the total so that the weights sum to one.

   $$w_j=\frac{s_j}{{\sum }_{k=1}^n{s}_k};\sum _{j=1}^n{w}_j=1$$
   LaTeX

   w_j = \frac{s_j}{\sum_{k=1}^{n} s_k}; \quad \sum_{j=1}^{n} w_j = 1

Sezgi

Sonucu okuma: Higher w_j = more important criterion. SIWEC advantage: experts do not need to rank or compare criteria pairwise - direct scoring suffices. The standard deviation σ_i reflects how much each expert differentiates between criteria; experts who rate all criteria equally contribute less weight.

Varsayımlar

• Domain experts available and willing to score criteria
• Experts can meaningfully differentiate between criteria (non-zero σ)

Ne zaman kullanılmaz

• No domain experts available - use objective weighting (CRITIC, ENTROPY)
• Experts tend to rate all criteria equally (zero variance problem)

Sık yapılan hatalar

• Tüm uzmanlar tüm kriterlere aynı puanı verirse σ_i=0 ve uzmanın katkısı sıfır olur.
• SIWEC öznel ağırlık üretir - uzman seçimine bağlı. Sağlamlık kontrolü için nesnel yöntemlerle (CRITIC, ENTROPY) birleştirin.