MCDMDecision-makingNormalizationMath steps

Vector Normalization — Euclidean column-norm scaling (L2 normalisation)

OriginatorHwang, C. L., Yoon, K.Year1981Sources1Related methods4

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

Strengths
  • 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.
Limitations
  • Results depend on the chosen normalisation, weights, and parameter settings.

Common pitfalls

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Sources

  1. 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