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Ranking
SF-VIKOR - Spherical extension of VIKOR
Spherical outranking/ranking - Spherical Fuzzy Set (SFS: μ, ν, π; μ²+ν²+π² ≤ 1)
Sharaf, I. M.2021doi:10.1007/978-3-030-45461-6_9 ↗
Overview
sf-vikor extends VIKOR 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, lower 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
- •Both absolute and relative ideal solutions supported; relative IS uses score-independent component-wise max/min hence robust to score-function choice.
- •γ tunes between group utility (γ→1) and individual regret (γ→0).
- •Stability + advantage tests reduce false-confident decisions.
Look elsewhere when
- •Crisp data sufficient - use base VIKOR 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
- •Q-ranking sensitive to γ choice; book uses γ=0.5 (consensus) by default but no sensitivity protocol mandated.
- •For absolute IS, d(X⁺,X⁻)=1 fixed - this can compress separation for very similar alternatives.
- •When acceptable-advantage fails, a set of compromise alternatives is returned - needs DM post-processing.
Edge cases and pitfalls
- •γ=1: yalnız utility ağırlıklı (regret göz ardı) - risk-tolerant DM için. γ=0: yalnız regret ağırlıklı (worst-case) - risk-averse DM için. γ=0.5: book default (consensus). S⁺=S⁻ veya R⁺=R⁻ durumunda Eq.18 paydası 0 - bu durumda Q tanımsız, alternatifler eşit kabul edilir. Accept-advantage başarısız: tüm Q⁽ᵏ⁾−Q⁽¹⁾<1/(n−1) olanlar uzlaşma kümesi olarak döner. Accept-stability başarısız ama advantage geçtiyse: yalnız Q⁽¹⁾ ve Q⁽²⁾ uzlaşma. Absolute IS d(X⁺,X⁻)=1 sabittir; relative IS'de değişir. SF-cell'in μ²+v²>1 olması imkansız (SFS tanımı ihlali) - validation'da yakalanmalı; relative NIS Eq.25'teki √(1−(μ²+v²)) düzeltmesi YALNIZ μ²_N+v²_N>1 olduğunda devreye girer.
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
Sharaf, I. M. (2021). Spherical Fuzzy VIKOR with SWAM and SWGM Operators for MCDM. 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_9
System ID, as it appears in reports and the API
SF-VIKOR