qR-VIKOR — q-Rung Orthopair extension of VIKOR
QR-VIKOR (qR-VIKOR — q-Rung Orthopair extension of VIKOR) 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-VIKOR lifts classical VIKOR (Opricovic 1998 / Opricovic-Tzeng 2004) into q-Rung Orthopair Fuzzy arithmetic. Cost criteria are converted to benefit via q-ROFN complement (μ, ν) → (ν, μ). Per-criterion positive- and negative-ideals are extracted coordinate-wise (f_j* = (max μ, min ν), f_j^- = (min μ, max ν)). The crisp gap (f_j*−x_ij)/(f_j*−f_j^-) is replaced by the q-ROF Euclidean distance ratio d_E(f_j*, a_ij) / d_E(f_j*, f_j^-) (Du 2018 distance, p=2). Group utility S_i (L_1) and individual regret R_i (L_∞) aggregate the weighted gaps. The compromise index Q_i = v·(S−S*)/(S^−−S*) + (1−v)·(
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-VIKOR — q-Rung Orthopair extension of VIKOR. ScholarGate. https://scholargate.app/en/decision-making/qr-vikor
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