qR-GRA - q-Rung Orthopair extension of GRA

Overview

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.

Output

utility, higher is better

Data

Q-Rung Orthopair Fuzzy, uncertainty tuples complete

Weights

Needs a weight source

Size

2+ alternatives, 3-10 criteria works best

Used for

Q-Rung Orthopair Fuzzy MCDM, MAGDM under epistemic uncertainty, expert-driven evaluation with linguistic terms

Look elsewhere when

Assumptions to verify

• Decision matrix entries are valid q-Rung Orthopair Fuzzy numbers/tuples
• Underlying crisp method's compensation assumption holds in uncertain space
• All decision-maker(s) and experts use the same linguistic/uncertainty scale

Edge cases and pitfalls

• •Single expert: skip F1 q-ROFWA aggregation; D_aggregated = D_1 directly.
• •Constant distance column (Δ_max = Δ_min, degenerate dataset): g_ab = 1 for all → Γ uniform → ranking by alternative_id (tie-handling fallback).
• •All-cost criteria: AD_b uses arg-min Liu-Wang score per cost criterion; no additional transformation at F1 needed.
• •Mixed q across cells: E-2 input check fails; Liu-Wang score and q-ROF distance are both q-dependent.
• •ρ outside [0,1]: warning issued; literature standard is ρ=0.5.

• Value-space violation: ensure all q-ROFN entries satisfy μ^q + ν^q ≤ 1 with the same q across matrix.

• Reference sequence definition: literature varies - some define AD via max-μ/min-ν component-wise, others via Liu-Wang score ordering. This manifest uses score-based ordering (consistent across Pattern A methods in the registry).

• Distinguishing coefficient ρ: literature standard is 0.5; values outside [0,1] are non-standard.

• Family difference: Güler 2026 anchor is q-RPF (3-tuple) but algorithm is structurally identical to q-ROF (drop η). Implementations must NOT introduce a neutral membership η that the user did not provide.

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