MCDMDecision-makingRankingMath steps

Interval extension of TOPSIS

OriginatorJahanshahloo, G. R., Lotfi, F. H., Izadikhah, M.Year2006Sources1Related methods8

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.

Key highlights

  • 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.

Intuition

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How it works

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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

Strengths
  • 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.
Limitations
  • 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.

Common pitfalls

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Sources

  1. 1.
    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

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ScholarGate. (2026, June 2). IV-TOPSIS. ScholarGate. https://scholargate.app/decision-making/iv-topsis