WSM: Weighted Sum Model (Simple Additive Weighting)

Overview

Additive utility: linear weighted sum. Output typically weighted_sum_score (higher value = preferred).

Strengths

• •Method-specific: Additive utility: linear weighted sum

Limitations

• •Assumes: Criteria are commensurate or have been pre-normalised (additive utility assumption).
• •Assumes: Compensation is acceptable: high score on one criterion can fully offset low on another.
• •Assumes: Criterion weights accurately reflect relative importance.
• •Assumes: Decision matrix is complete (no missing values).

Assumptions to verify

• •Criteria are commensurate or have been pre-normalised (additive utility assumption).
• •Compensation is acceptable: high score on one criterion can fully offset low on another.
• •Criterion weights accurately reflect relative importance.
• •Decision matrix is complete (no missing values).

When not to use

• •Criteria have strongly different units without normalisation → violates additive utility.
• •Non-compensatory preferences required → use ELECTRE or PROMETHEE.
• •Strong criterion interactions (synergies/antagonisms) → use ANP or Choquet integral.

Edge cases

• •If all criteria are already in the same unit and all max, this step may be skipped (as in Triantaphyllou 2000 Example 2-1 which uses raw values directly).

Common pitfalls

• •Hatalı: 'WSM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria are commensurate or have been pre-normalised (additive utility assumption).
• •Hatalı: 'WSM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can fully offset low on another.
• •Hatalı: 'WSM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criterion weights accurately reflect relative importance.
• •Hatalı: 'WSM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values).
• •Hatalı: WSM'yi 'Criteria have strongly different units without normalisation → violates additive utility.' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: WSM'yi 'Non-compensatory preferences required → use ELECTRE or PROMETHEE.' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: WSM'yi 'Strong criterion interactions (synergies/antagonisms) → use ANP or Choquet integral.' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Direction-aware linear normalisation: for max criteria map to [0,1] by (x−min)/(max−min); for min criteria invert by (max−x)/(max−min). If all criteria are already in the same unit and all max, this step may be skipped (as in Triantaphyllou 2000 Example 2-1 which uses raw values directly). Formül: r_{ij} = \begin{cases} x_{ij} & \text{if all } j\in J^{+} \text{ and same unit (Triantaphyllou 2000 Eq.(2-1) shortcut)} \\[6pt] \dfrac{x_{ij} - \min_i x_{ij}}{\max_i x_{ij} - \min_i x_{ij}} & j \in J^{+} \text{ (engineering normalisation, mixed units)} \\[6pt] \dfrac{\max_i x_{ij} - x_{ij}}{\max_i x_{ij} - \min_i x_{ij}} & j \in J^{-} \text{ (engineering normalisation, mixed units)} \end{cases} Anchor: Fishburn 1967 Operations Research 15(3):537-542; Triantaphyllou 2000 Ch.2 §2.2.1 Eq.(2-1)
2. 2.Adım 2 (F2): Step 2: Compute WSM score for each alternative: weighted sum of normalised performance values. Higher score = better. Rank alternatives by descending score. Formül: \text{score}_i = \sum_{j=1}^{n} w_j \cdot r_{ij},\quad i=1,\ldots,m Anchor: Fishburn 1967 Operations Research 15(3):537-542 Eq.(1); Triantaphyllou 2000 Ch.2 §2.2.1 Eq.(2-1)

Commonly paired with

• •AHP + WSM (high)
• •ENTROPY + WSM (high)
• •CRITIC + WSM (high)
• •SWARA + WSM (medium)

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