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Ranking
SF-WASPAS - Spherical extension of WASPAS
Spherical outranking/ranking - Spherical Fuzzy Set (SFS: μ, ν, π; μ²+ν²+π² ≤ 1)
Boltürk, E., Kutlu Gündoğdu, F.2021doi:10.1007/978-3-030-45461-6_11 ↗
Overview
sf-waspas extends WASPAS 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
- •λ-tunable mix of WSM/WPM captures both decision-aggregation philosophies.
- •Eq.24 SF-aggregation preserves hesitancy through both branches.
- •Default λ=0.5 (equal mix) is decisional-neutral and matches Zavadskas-Turskis 2012 crisp WASPAS.
Look elsewhere when
- •Crisp data sufficient - use base WASPAS 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
- •λ-choice is a meta-decision that can dominate ranking if S/R measures differ widely.
- •Two aggregation passes (WSM+WPM) double the computational/notation burden.
- •No formal rule for choosing λ - book Recommends 0.5 but offers no optimization.
Edge cases and pitfalls
- •λ=1 pure WSM (SF-SAW eşdeğeri); λ=0 pure WPM (SF-WPM eşdeğeri); λ=0.5 book default consensus. Bir alt çok düşük μ'lu cell'e sahipse: WPM partı (Q̃^(2)) sert cezalandırır, WSM partı (Q̃^(1)) yumuşatır - λ=0.5'te ikisi karışır. SWAM vs SWGM seçimi: SWAM additive-mean (DM görüşleri toplamsal), SWGM geometric-mean (DM görüşleri multiplicative). Book Section 4 SWGM kullanır ağırlık için (Tablo 6). λ-power Eq.20 (w̄^s_j üs): w̄^s_j fraksiyonel olduğunda Eq.6 dikkatli - π=0 edge case test. Modified Score Eq.14 negatif (yüksek v + yüksek π) durumunda Eq.15 normalize problem.
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
Boltürk, E.; Kutlu Gündoğdu, F. (2021). Prioritizing Manufacturing Challenges of a Contract Manufacturing Company for Personal Auto by Using Spherical WASPAS Method. 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_11
System ID, as it appears in reports and the API
SF-WASPAS