Complex extension of TOPSIS
CF-TOPSIS (Complex extension of TOPSIS) is a ranking multi-criteria decision-making (MCDM) method introduced by Ramot, D. Milo, R. Friedman, M. Kandel, A. in 2002. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
When to use it
cf-topsis extends TOPSIS to handle Complex uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Complex Fuzzy Set (CFS: amplitude r ∈ [0,1], phase ω ∈ [0,2π]) algebra. The final scores are defuzzified via real part: r·cos(ω) before ranking.
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
- Ramot, D., Milo, R., Friedman, M., Kandel, A. (2002). Complex fuzzy sets. IEEE Transactions on Fuzzy Systems DOI: 10.1109/91.995119 ↗
How to cite this page
ScholarGate. (2026, June 2). Complex extension of TOPSIS. ScholarGate. https://scholargate.app/en/decision-making/cf-topsis
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- AHPDecision-making↔ compare
- ANPDecision-making↔ compare
- BWMDecision-making↔ compare
- BWM-BAYESIANDecision-making↔ compare
- CCSDDecision-making↔ compare
- CILOSDecision-making↔ compare
- CIMASDecision-making↔ compare
- CRITICDecision-making↔ compare