Standard Deviation Weight: objective weighting by column standard deviation

Overview

Weight_Objective. Output typically weight (higher value = preferred).

Strengths

• •Method-specific: Weight_Objective

Limitations

• •Assumes: Decision matrix exists with measurable criteria
• •Assumes: Sufficient inter-alternative variation per criterion

Assumptions to verify

• •Decision matrix exists with measurable criteria
• •Sufficient inter-alternative variation per criterion

When not to use

• •No data variation (constant criterion) → weight degenerates
• •Expert judgment is the actual driver → use subjective weighting

Edge cases

• •See F.steps and D.parameters for SD-WEIGHT-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

• •Hatalı: 'SD-WEIGHT bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix exists with measurable criteria
• •Hatalı: 'SD-WEIGHT bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Sufficient inter-alternative variation per criterion
• •Hatalı: SD-WEIGHT'yi 'No data variation (constant criterion) → weight degenerates' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: SD-WEIGHT'yi 'Expert judgment is the actual driver → use subjective weighting' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Normalise decision matrix using min-max (direction-aware). Formül: r_{ij}=(x_{ij}-x_j^{\min})/(x_j^{\max}-x_j^{\min})\text{ (benefit)} Anchor: Standard MCDM normalisation (pending PDF page verification)
2. 2.Adım 2 (F2): Step 2: Compute population standard deviation σ_j of each normalised column. Normalise: w_j = σ_j / Σ σ_k. Formül: \sigma_j = \sqrt{\frac{1}{m}\sum_i(r_{ij}-\bar{r}_j)^2};\quad w_j = \sigma_j/\sum_k\sigma_k Anchor: Standard MCDM weighting (pending PDF page verification)

Commonly paired with

• •SD-WEIGHT + TOPSIS (high)
• •SD-WEIGHT + VIKOR (high)
• •SD-WEIGHT + EDAS (high)
• •SD-WEIGHT + WASPAS (high)
• •SD-WEIGHT + MARCOS (high)

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