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Ranking
SF-SAW - Spherical extension of SAW
Spherical outranking/ranking - Spherical Fuzzy Set (SFS: μ, ν, π; μ²+ν²+π² ≤ 1)
Kutlu Gündoğdu, F., Yörükoğlu, M.2021doi:10.1007/978-3-030-45461-6_10 ↗
Overview
sf-saw extends SAW to handle Spherical uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Spherical Fuzzy Set (SFS: μ, ν, π; μ²+ν²+π² ≤ 1) algebra. The final scores are defuzzified via score function S = μ² − ν² before ranking.
- Output
- utility, higher is better
- Data
- Spherical Fuzzy, uncertainty tuples complete
- Weights
- Needs a weight source
- Size
- 2+ alternatives, 3-10 criteria works best
- Used for
- Spherical Fuzzy MCDM, MAGDM under epistemic uncertainty, expert-driven evaluation with linguistic terms
Fits when / Look elsewhere when
Fits when
- •Simplest SF aggregation: scalar-multiply + add, no PIS/NIS needed.
- •Score Eq.30 (3μ−π/2)²−(v−π/2)² has explicit hesitancy penalty.
- •Computational footprint minimal.
Look elsewhere when
- •Crisp data sufficient - use base SAW directly (avoid unnecessary uncertainty layer)
- •Aggregation operator (PFWA/PFOWA/etc.) not specified - output ambiguous
Assumptions to verify
- Decision matrix entries are valid Spherical Fuzzy numbers/tuples
- Underlying crisp method's compensation assumption holds in uncertain space
- All decision-maker(s) and experts use the same linguistic/uncertainty scale
Limitations
- •Implicit normalization assumption: cost criteria must be reframed as benefit (e.g., "low price"→"good price").
- •No compensation control - high-μ on one criterion can mask high-v on another.
- •Modified-score form (3μ vs 2μ) is method-specific; mixing scores across methods causes inconsistency.
Edge cases and pitfalls
- •Tüm ağırlıklar eşit (w̃_j hepsi aynı): SVSAW basit ortalama olur. Bir kriter'in ağırlığı 0 (defuzzified): o kriter ranking'e katkı vermez. SF cell'de μ→0: SVSAW cell katkısı 0'a yaklaşır (additive olduğu için multiplicative WPM'den farkı bu - küçük μ değil sıfır olmalı silici etki için). Cost criteria için: book yaklaşımı "DMs assign lower linguistic term" - Step 3 notu. Modified Score Eq.30 negatif çıkabilir (yüksek v + yüksek π); negatif normalize Eq.31 problemli - Eq.31'de paydanın pozitif olduğunu garantilemek için tüm S(w̃)>0 olmalı. Bir DM çok düşük μ verirse (neredeyse 0): SWAM'da o DM'in katkısı baskılanır (SWAM Eq.7'de Π(1−μ²)^w çarpan yapısı).
Value-space violation: ensure all entries satisfy SFS: μ,ν,π ∈ [0,1]; μ²+ν²+π² ≤ 1 before computation.
Defuzzification method affects ranking: score function S = μ² − ν² is the canonical choice but alternatives exist.
Works with
Commonly takes its weights from
How to cite
Kutlu Gündoğdu, F.; Yörükoğlu, M. (2021). Simple Additive Weighting and Weighted Product Methods Using Spherical Fuzzy Sets. In: Kahraman C., Kutlu Gündoğdu F. (eds.) Decision Making with Spherical Fuzzy Sets - Theory and Applications. Studies in Fuzziness and Soft Computing vol. 392. Springer. https://doi.org/10.1007/978-3-030-45461-6_10
System ID, as it appears in reports and the API
SF-SAW