Vector Normalization — Euclidean column-norm scaling (L2 normalisation)
NORM-VECTOR (Vector Normalization — Euclidean column-norm scaling (L2 normalisation)) is a normalization multi-criteria decision-making (MCDM) method introduced by Hwang, C. L., Yoon, K. in 1981. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.
Key highlights
- Follows a transparent, reproducible computational procedure that can be audited step by step.
- Handles multiple criteria of differing scales and units within a single decision matrix.
Intuition
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How it works
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When to use it
After vector normalisation, each column has unit Euclidean norm (Σ_i r_ij² = 1). The normalised values preserve the ratio structure of the original data. Cost/benefit direction is NOT applied during this step — it must be handled downstream (e.g. by selecting A⁺/A⁻ in TOPSIS).
Strengths & limitations
- Follows a transparent, reproducible computational procedure that can be audited step by step.
- Handles multiple criteria of differing scales and units within a single decision matrix.
- Results depend on the chosen normalisation, weights, and parameter settings.
Common pitfalls
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Sources
- 1.Hwang, C. L., Yoon, K. (1981). Multiple Attribute Decision Making: Methods and Applications. Lecture Notes in Economics and Mathematical Systems, Vol. 186, Springer-Verlag
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ScholarGate. (2026, June 2). NORM-VECTOR. ScholarGate. https://scholargate.app/decision-making/norm-vector