Standard Deviation Weight - objective weighting by column standard deviation

Overview

SD weighting assigns higher weight to criteria with greater discrimination power (higher variance across alternatives after normalisation). Criteria where all alternatives perform similarly get low weight. Unlike CRITIC/CCSD it ignores inter-criterion correlation.

Output

Weight, higher is better

Data

Crisp, complete numeric matrix

Weights

Derived internally, no weight source needed

Size

2+ alternatives, 3-12 criteria works best

Used for

Any (objective weighting)

How it works

1. 1

   Normalise decision matrix using min-max (direction-aware).

   $$r_{ij}=(x_{ij}-x_j^{\min })/(x_j^{\max }-x_j^{\min })\text{ (benefit)}$$

   Standard MCDM normalisation (pending PDF page verification)

2. 2

   Compute population standard deviation σ_j of each normalised column. Normalise: w_j = σ_j / Σ σ_k.

   $${\sigma }_j=\sqrt{\frac{1}{m}\sum _i(r_{ij}-{\bar{r}}_j{)}^2};w_j={\sigma }_j/\sum _k{\sigma }_k$$

   Standard MCDM weighting (pending PDF page verification)

Look elsewhere when

Assumptions to verify

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

Edge cases and pitfalls

• Constant column: σ_j=0 → w_j=0. Check for degenerate columns before applying.

Works with

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