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Ranking
SF-CODAS - Spherical extension of CODAS
Spherical outranking/ranking - Spherical Fuzzy Set (SFS: μ, ν, π; μ²+ν²+π² ≤ 1)
Karaşan, A., Boltürk, E., Kutlu Gündoğdu, F.2021doi:10.1007/978-3-030-45461-6_12 ↗
Overview
sf-codas extends CODAS 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
- •Two-distance design (Euclidean primary + spherical/arccos secondary) reduces tie ambiguity.
- •α-threshold (default 0.02) is decision-tunable.
- •Sensitivity over α gives DM a clear robustness picture.
Look elsewhere when
- •Crisp data sufficient - use base CODAS 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
- •NIS-only logic ignores PIS information - sometimes counter-intuitive (alternative very close to PIS but not far from NIS may rank low).
- •Spherical (arccos) distance numerical noise near surface boundary may distort tie-breaking for very similar SFSs.
- •α-choice not optimized; book uses 0.02 by convention.
Edge cases and pitfalls
- •α=0.02 default - tüm |D_E_i−D_E_k|≥α durumunda spherical distance tie-breaker olarak devreye girer. α=0 tüm tie'lar açılır (spherical her zaman aktif). α=1 spherical asla devreye girmez (yalnız Öklid). Sensitivity: book Fig.2 α∈[0,0.125]'te ranking stabil, üzerinde X_2-X_5 swap. NIS dejenere (tüm cell'ler aynı score): D_E_i=0 her i için → AS_i=0 her i için → tüm tie. SF-cell'de π≈1, μ,v≈0: Eq.20 score ≈ −0.25 (NIS aday). Spherical distance Eq.24 SF'lerin küresel yüzeyinde "açısal mesafe" - çok yakın SFS'ler için arccos near-zero, küçük μ-v farkları amplified. PIS KULLANILMAZ - TOPSIS'ten farkı bu.
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
Karaşan, A.; Boltürk, E.; Kutlu Gündoğdu, F. (2021). Assessment of Livability Indices of Suburban Places of Istanbul by Using Spherical Fuzzy CODAS 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_12
System ID, as it appears in reports and the API
SF-CODAS