MCDMDecision-makingRankingMath steps

Spherical extension of TOPSIS

OriginatorKutlu Gündoğdu & KahramanYear2019Sources1Related methods8

SF-TOPSIS (Spherical extension of TOPSIS) is a ranking multi-criteria decision-making (MCDM) method introduced by Kutlu Gündoğdu & Kahraman in 2019. 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

SF-TOPSIS (Kutlu Gündoğdu & Kahraman 2019) extends TOPSIS to Spherical Fuzzy Sets (μ²+ν²+π² ≤ 1, hesitancy π independent). Pipeline: SWAM/SWGM aggregation of DM judgments → weighted SF matrix via SF multiplication ⊗ → defuzzify by score S(α) = (μ−π)² − (ν−π)² → SF-PIS / SF-NIS extraction (max/min score per criterion) → normalized Euclidean SF distance D(X, X*) and D(X, X⁻) (factor 1/(2n)) → revised closeness ratio ξ(X) = D(X,X*)/D_min(X,X*) − D(X,X⁻)/D_max(X,X⁻) → ASCENDING rank (smaller ξ = better).

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.
    Kutlu Gündoğdu, F., Kahraman, C. (2019). Spherical fuzzy sets and spherical fuzzy TOPSIS method. Journal of Intelligent & Fuzzy Systems

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Cite this page

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

Spherical extension of TOPSIS | ScholarGate