Linear Max Normalization — division by column maximum (benefit) or column minimum over value (cost)
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.
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Method map
The neighbourhood of related methods — select a node to explore.
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
- 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.
Sources
- Fishburn, P. C. (1967). Additive Utilities with Incomplete Product Sets: Application to Priorities and Assignments. Operations Research DOI: 10.1287/opre.15.3.537 ↗
How to cite this page
ScholarGate. (2026, June 2). Linear Max Normalization — division by column maximum (benefit) or column minimum over value (cost). ScholarGate. https://scholargate.app/en/decision-making/linear-max-normalization
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- ARASDecision-making↔ compare
- COPRASDecision-making↔ compare
- MARCOSDecision-making↔ compare
- WPMDecision-making↔ compare