qR-COPRAS: q-Rung Orthopair extension of COPRAS

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 COPRAS directly (avoid unnecessary uncertainty layer)
• •Aggregation operator (PFWA/PFOWA/etc.) not specified: output ambiguous

Edge cases

• •All-benefit (Ω_c=∅): Q_i=S_i^+ fallback; ranking identical to q-ROF SAW under all-benefit inputs.
• •All-cost (Ω_b=∅): Q_i=(Σ_k S_k^-)/(S_i^- · Σ_k(1/S_k^-)); smaller cost wins.
• •S_k^-=0 for some k: engine adds ε=1e-12 to all S_k^- before harmonic mean to avoid division-by-zero.
• •Mixed q across cells: E-2 input check fails; Liu-Wang score is q-dependent, mixed q produces incomparable scores.

Common pitfalls

• •Pitfall 1: Handling cost direction via q-ROFN complement (μ,ν)^c=(ν,μ) at F1. WRONG: the s+1 shift assumes original-sign scores; flipping at F1 double-flips cost criteria. Correct: partition Ω_b/Ω_c at F2.
• •Pitfall 2: Using Peng-Huang 2020 hesitancy-penalty score r(α)=μ^q−ν^q−ln(1+π^q) without re-documenting. This manifest uses Liu-Wang 2018 plain score; switching scores changes ranking under hesitancy-heavy inputs.
• •Pitfall 3: Citing this manifest as 'q-ROF COPRAS paper-anchored': IT IS NOT. Until a pure q-ROF COPRAS application paper is anchored, cite as 'tex+Liu-Wang+Zavadskas Pattern B fusion' and acknowledge methodological gap.
• •Pitfall 4: Mixing q values across cells. q is a global matrix parameter (J.extra_inputs.q); engine E-2 enforces single q.
• •Pitfall 5: Confusing this with Zavadskas-Kaklauskas 1996 crisp COPRAS: the manifold method ID is QR-COPRAS not COPRAS. Manifest 'conflicts_with' lists COPRAS (do not chain both).

Commonly paired with

• •n_a + QR-COPRAS (common)

How to cite