Z-Number extension of TOPSIS
Z-TOPSIS (Z-Number extension of TOPSIS) is a ranking multi-criteria decision-making (MCDM) method introduced by Gardashova, L. A. in 2018. 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
z-topsis extends TOPSIS to handle Z-Number uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Z-Number (Z = (A, B): restriction A, reliability B; both fuzzy) algebra. The final scores are defuzzified via convert to regular fuzzy: Ã = B·A, then centroid 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.
Common pitfalls
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Sources
- 1.Gardashova, L. A. (2018). Z-Number Based TOPSIS Method in Multi-Criteria Decision Making. Advances in Intelligent Systems and Computing
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ScholarGate. (2026, June 2). Z-TOPSIS. ScholarGate. https://scholargate.app/decision-making/z-topsis