Grey Relational Analysis
GRA (Grey Relational Analysis) is a ranking multi-criteria decision-making (MCDM) method introduced by Deng, J. L. in 1989. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.
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When to use it
Γ_i ∈ (0,1]. Higher Γ means greater similarity to the ideal reference sequence. ζ=0.5 is Deng's recommended default — it balances the contribution of the minimum and maximum absolute differences. Smaller ζ amplifies the discriminating power (differences between alternatives become larger); larger ζ reduces discrimination.
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.
- Assumes full compensation — a strong score on one criterion can offset a weak score on another.
Sources
- Deng, J. L. (1989). Introduction to grey system theory. The Journal of Grey System DOI: 10.5555/90757.90758 ↗
How to cite this page
ScholarGate. (2026, June 2). Grey Relational Analysis. ScholarGate. https://scholargate.app/en/decision-making/gra
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.
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