Pythagorean extension of TOPSIS
PF-TOPSIS (Pythagorean extension of TOPSIS) is a ranking multi-criteria decision-making (MCDM) method introduced by Zhang, X., Xu, Z. in 2014. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.
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When to use it
pf-topsis extends TOPSIS to handle Pythagorean uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Pythagorean Fuzzy Number (PFN: μ, ν; μ²+ν² ≤ 1) algebra. The final scores are defuzzified via score function S = μ² − ν² 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
- Zhang, X., Xu, Z. (2014). Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets. International Journal of Intelligent Systems DOI: 10.1002/int.21676 ↗
How to cite this page
ScholarGate. (2026, June 2). Pythagorean extension of TOPSIS. ScholarGate. https://scholargate.app/en/decision-making/pf-topsis
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