qR-COPRAS — q-Rung Orthopair extension of COPRAS
QR-COPRAS (qR-COPRAS — q-Rung Orthopair extension of COPRAS) is a ranking multi-criteria decision-making (MCDM) method introduced by Yager, R. R. in 2017. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.
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When to use it
QR-COPRAS Pattern B: each q-ROFN cell is reduced to a crisp score s_ij = μ^q − ν^q at F1, shifted to [0, 2] via s̃ = s + 1 (so the cost denominator in F3 stays positive), column-sum normalised, and weighted. F2 splits the weighted row into benefit (S_i^+) and cost (S_i^-) sums. F3 computes Q_i = S_i^+ + (Σ_k S_k^-)/(S_i^- · Σ_k(1/S_k^-)) — the larger Q_i, the better. F4 reports N_i = Q_i / max Q × 100% as a utility-degree summary. Ranking is descending in Q_i (equivalently, in N_i). Cost direction is handled by the Ω_c partition at F2, NOT by q-ROFN complement at F1 (the s + 1 shift assumes sc
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.
- May exhibit rank reversal when alternatives are added to or removed from the set.
- Assumes full compensation — a strong score on one criterion can offset a weak score on another.
Sources
- Yager, R. R. (2017). Generalized orthopair fuzzy sets. IEEE Transactions on Fuzzy Systems DOI: 10.1109/TFUZZ.2016.2604005 ↗
How to cite this page
ScholarGate. (2026, June 2). qR-COPRAS — q-Rung Orthopair extension of COPRAS. ScholarGate. https://scholargate.app/en/decision-making/qr-copras
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