MCDMDecision-makingNormalizationMath steps

Linear Max Normalization — division by column maximum (benefit) or column minimum over value (cost)

OriginatorFishburn, P. C.Year1967Sources1Related methods4

LINEAR-MAX-NORMALIZATION (Linear Max Normalization — division by column maximum (benefit) or column minimum over value (cost)) is a normalization multi-criteria decision-making (MCDM) method introduced by Fishburn, P. C. in 1967. 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

r_ij ∈ (0,1] for positive data. The best alternative always scores 1. Unlike min-max, the worst alternative does not necessarily score 0. Used in ARAS, COPRAS, WPM.

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.
    Fishburn, P. C. (1967). Additive Utilities with Incomplete Product Sets: Application to Priorities and Assignments. Operations Research

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ScholarGate. (2026, June 2). LINEAR-MAX-NORMALIZATION. ScholarGate. https://scholargate.app/decision-making/linear-max-normalization