MCDMDecision-makingRankingMath steps

qR-GRA — q-Rung Orthopair extension of GRA

OriginatorYager, R. R.Year1989Sources1Related methods8

QR-GRA (qR-GRA — q-Rung Orthopair extension of GRA) is a ranking multi-criteria decision-making (MCDM) method introduced by Yager, R. R. in 1989. 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

qR-GRA uses Pattern A (q-ROF aggregation kept fuzzy until distance step): expert q-ROFN matrices are aggregated via q-ROFWA, then a reference q-ROFN sequence AD_b is extracted per criterion (max-Liu-Wang-score row for benefit, min for cost). q-ROF Euclidean distance Δ_ab to AD_b is computed (Du 2018 / Güler 2026 Eq.20 with η=0). Grey relational coefficient g_ab uses distinguishing coefficient ρ=0.5. Final grade Γ_a = Σ w_b · g_ab ∈ [0,1] is crisp.

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
  • Assumes full compensation — a strong score on one criterion can offset a weak score on another.

Common pitfalls

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Sources

  1. 1.
    Yager, R. R. (2017). Generalized orthopair fuzzy sets. IEEE Transactions on Fuzzy Systems

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ScholarGate. (2026, June 2). QR-GRA. ScholarGate. https://scholargate.app/decision-making/qr-gra