Rough-TOPSIS — Rough extension of TOPSIS
ROUGH-TOPSIS (Rough-TOPSIS — Rough extension of TOPSIS) is a ranking multi-criteria decision-making (MCDM) method introduced by Song, W. Ming, X. Wu, Z. in 2013. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.
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When to use it
ROUGH-TOPSIS (Song, Ming & Wu 2013) is NOT standard TOPSIS adapted to rough numbers. It uses a deviation-coefficient approach: (1) PIS/NIS are crisp scalars from raw matrix bound extremes (no normalization); (2) rough deviation coefficients d+/d− are linear distances (not Euclidean); (3) deviations are normalized per criterion by column max upper bound; (4) separation measures S+/S− are rough intervals from weighted normalized deviations; (5) final CC uses α-defuzzification: S+*=(1-α)S+L+αS+U, S−*=αS−L+(1-α)S−U; CC=S−*/(S−*+S+*); rank descending. α=0.5 = moderate risk propensity.
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
- Song, W., Ming, X., Wu, Z. (2013). An integrated rough number-based approach to design concept evaluation under subjective environments. International Journal of Computer Integrated Manufacturing DOI: 10.1080/09544828.2012.732994 ↗
How to cite this page
ScholarGate. (2026, June 2). Rough-TOPSIS — Rough extension of TOPSIS. ScholarGate. https://scholargate.app/en/decision-making/rough-topsis
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