SF-MABAC

SF-MABAC - MABAC yönteminin Spherical uzantısı

Spherical üstünlük/sıralama - Küresel Bulanık Küme (KBK: μ, ν, π; μ²+ν²+π² ≤ 1)

Formül adımları

Analiz motorunun yöntem bildirimindeki (manifest F.steps) adımlar; raporlardaki formüllerle aynı kaynaktır.

normalization

${\tilde{a}}_{i j}^{c} = (ν_{i j}, μ_{i j}, π_{i j}) for cost criteria$

LaTeX
\tilde{a}_{ij}^{c}=(\nu_{ij},\mu_{ij},\pi_{ij})\quad\text{for cost criteria}
aggregation

${\tilde{v}}_{i j} = w_{j} {\tilde{a}}_{i j} = (\sqrt{1 - (1 - μ_{i j}^{2})^{w_{j}}}, ν_{i j}^{w_{j}}, \sqrt{(1 - μ_{i j}^{2})^{w_{j}} - (1 - μ_{i j}^{2} - π_{i j}^{2})^{w_{j}}})$

LaTeX
\tilde{v}_{ij}=w_j\tilde{a}_{ij}=\Bigl(\sqrt{1-(1-\mu_{ij}^2)^{w_j}},\;\nu_{ij}^{w_j},\;\sqrt{(1-\mu_{ij}^2)^{w_j}-(1-\mu_{ij}^2-\pi_{ij}^2)^{w_j}}\Bigr)
ranking_computation

$s ({\tilde{g}}_{j}) = \frac{1}{m} \sum_{i = 1}^{m} s ({\tilde{v}}_{i j}), s ({\tilde{v}}_{i j}) = \frac{1}{3} (2 + μ_{i j} - ν_{i j} - π_{i j})$

LaTeX
s(\tilde{g}_j)=\frac{1}{m}\sum_{i=1}^m s(\tilde{v}_{ij}),\quad s(\tilde{v}_{ij})=\frac{1}{3}(2+\mu_{ij}-\nu_{ij}-\pi_{ij})
ranking_computation

$q_{i j} = s ({\tilde{v}}_{i j}) - s ({\tilde{g}}_{j})$

LaTeX
q_{ij}=s(\tilde{v}_{ij})-s(\tilde{g}_j)
ranking_computation

$S_{i} = \sum_{j = 1}^{n} q_{i j}, rank descending$

LaTeX
S_i=\sum_{j=1}^n q_{ij},\quad\text{rank descending}

Yöntem ayrıntıları kaynak kütüphanedeki özgün (İngilizce) metindir.

Sezgi

Sonucu okuma: sf-mabac extends MABAC 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.

Varsayımlar

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

Ne zaman kullanılmaz

Classical data sufficient - use base MABAC directly (avoid unnecessary uncertainty layer)
Aggregation operator (PFWA/PFOWA/etc.) not specified - output ambiguous

Sık yapılan hatalar

Değer-uzayı ihlali: hesaplamadan önce tüm girişlerin SFS: μ,ν,π ∈ [0,1]; μ²+ν²+π² ≤ 1 koşulunu sağladığından emin olun.
Defuzzifikasyon yöntemi sıralamayı etkiler: score function S = μ² − ν² kanonik seçimdir.