MCDMDecision-makingNormalizationMath steps
Z-Score Normalization — standardisation to zero mean and unit standard deviation
Z-SCORE-NORMALIZATION (Z-Score Normalization — standardisation to zero mean and unit standard deviation) is a normalization multi-criteria decision-making (MCDM) method introduced by Hellwig, Z. in 1968. 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
z_ij ∈ (−∞,+∞); columns have mean=0 and population σ=1. Handles negative values and large-scale differences. The cost flip ensures higher z = better. Used in HELLWIG method and TAXONOMY.
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.Hellwig, Z. (1968). Zastosowanie metody taksonomicznej do typologicznego podzialu krajow ze wzgledu na poziom ich rozwoju oraz zasoby i strukture wykwalifikowanych kadr technicznych. Przeglad Statystyczny
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Cite this page
ScholarGate. (2026, June 2). Z-SCORE-NORMALIZATION. ScholarGate. https://scholargate.app/decision-making/z-score-normalization