qR-GRA: q-Rung Orthopair extension of GRA

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

When not to use

• •Crisp data sufficient: use base GRA directly (avoid unnecessary uncertainty layer)
• •Aggregation operator (PFWA/PFOWA/etc.) not specified: output ambiguous

Edge cases

• •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.

Common pitfalls

• •Pitfall 1: Applying q-ROFN complement (μ,ν)^c=(ν,μ) for cost direction at F1 (aggregation) instead of F3 (reference extraction). WRONG: q-ROFWA on complemented matrices loses the original sign convention. Correct: keep matrix as-is through F1; use arg-min Liu-Wang score for cost criteria at F3.
• •Pitfall 2: Using .tex's 3-term distance (with π^q hesitancy term) without re-documenting. This manifest uses Güler 2026 / Du 2018 2-term distance (η-drop equivalent); switching to 3-term changes rankings under hesitancy-heavy inputs.
• •Pitfall 3: Citing Güler 2026 as if it were a 'pure q-ROF GRA paper': IT IS q-RPF (q-Rung PICTURE Fuzzy, 3-tuple with neutral membership η). The manifest drops η for q-ROF compatibility; cite accurately as 'Pattern A adapted from Güler 2026 q-RPF GRA via η-drop'.
• •Pitfall 4: Citing Ahemad 2023 as 'pure q-ROF': IT IS IVq-ROF (interval-valued). Pure q-ROF version requires degenerate intervals [μ,μ]/[ν,ν].
• •Pitfall 5: Citing Garg 2022 Ch.2 as 'pure q-ROF GRA': Ch.2 is q-ROFSS (soft set wrapper). GRA skeleton is the same but the input data type differs.
• •Pitfall 6: Confusing this with Deng 1989 crisp GRA: the manifold method ID is QR-GRA not GRA. Manifest 'conflicts_with' lists GRA (do not chain both).
• •Pitfall 7 (audit history): Pre-2026-05-21 versions included a Wei 2021 LITERATURE-RECALL placeholder entry in B.extensions with empty doi/file_ref: REMOVED 2026-05-21 per /bilim-modu STOP condition (paper inaccessible → no canonical claim).

Commonly paired with

• •n_a + QR-GRA (common)

How to cite