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Ranking
Rough-VIKOR - Rough extension of VIKOR
Rough outranking/ranking - Rough number (lower approximation L, upper approximation U)
Zhu, G., Hu, J., Qi, J., Gu, C., Peng, Y.2015doi:10.1016/j.aei.2015.01.010 ↗
Overview
ROUGH-VIKOR (Zhu et al. 2015) extends VIKOR to rough [L,U] intervals. PIS/NIS (f*/f-) are crisp scalars derived from bound extremes - no defuzzification at this step. S and R are rough intervals computed via bound-specific ratio arithmetic (w^L with ratio^L, w^U with ratio^U). Rough Q [L,U] is computed component-wise using crisp extremes S*/S^-/R*/R^-. Final ranking is by Q midpoint (L+U)/2 ascending - lower Q means better rank.
- Output
- utility, lower is better
- Data
- Rough Number, uncertainty tuples complete
- Weights
- Needs a weight source
- Size
- 2+ alternatives, 3-10 criteria works best
- Used for
- Rough MCDM, MAGDM under epistemic uncertainty, expert-driven evaluation with linguistic terms
Look elsewhere when
- •Crisp data sufficient - use base VIKOR directly (avoid unnecessary uncertainty layer)
- •Aggregation operator (PFWA/PFOWA/etc.) not specified - output ambiguous
Assumptions to verify
- Decision matrix entries are valid Rough 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
Value-space violation: ensure all entries satisfy Rough: L ≤ U; approximations defined by equivalence classes before computation.
Defuzzification method affects ranking: midpoint (L+U)/2 is the canonical choice but alternatives exist.
Works with
Commonly takes its weights from
How to cite
Zhu, G.; Hu, J.; Qi, J.; Gu, C.; Peng, Y. (2015). An integrated AHP and VIKOR for design concept evaluation based on rough number. Advanced Engineering Informatics. https://doi.org/10.1016/j.aei.2015.01.010
System ID, as it appears in reports and the API
ROUGH-VIKOR