Interval extension of TOPSIS
IV-TOPSIS (Interval extension of TOPSIS) is a ranking multi-criteria decision-making (MCDM) method introduced by Jahanshahloo, G. R., Lotfi, F. H., Izadikhah, M. in 2006. 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
IV-TOPSIS extends crisp TOPSIS to bounded uncertainty represented as Interval Numbers IN: [L, U]. The Jahanshahloo–Lotfi–Izadikhah (2006) algorithm keeps both bounds throughout normalisation and weighting; the positive- and negative-ideal solutions are then assembled by taking max/min over the appropriate bound depending on whether each criterion is a benefit or a cost. Distances use the opposite bound (lower for d⁺ on benefits, upper for d⁻ on benefits, swapped for costs) so that the worst-case separation is measured. The final relative closeness C* is a crisp scalar in [0, 1] — no defuzzific
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
- Jahanshahloo, G. R., Lotfi, F. H., Izadikhah, M. (2006). An algorithmic method to extend TOPSIS for decision-making problems with interval data. Applied Mathematics and Computation DOI: 10.1016/j.amc.2005.08.048 ↗
How to cite this page
ScholarGate. (2026, June 2). Interval extension of TOPSIS. ScholarGate. https://scholargate.app/en/decision-making/iv-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