CFZN-WASPAS - Karmaşık Bulanık Z-Sayıları Ağırlıklı Birleştirilmiş Toplam Çarpım Değerlendirmesi

Formül adımları

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

CFZN karar matrisi, kriter ağırlıkları, yön vektörü ve WASPAS birleştirme katsayısı ϒ'yi doğrula.

$T = [T_{i j}]_{m \times n}, T_{i j} = {σ_{i j} e^{2 π i τ_{i j}}, ϖ_{i j} e^{2 π i ℜ_{i j}}}; w = (w_{1}, \dots, w_{n}), \sum w_{j} = 1; Υ \in [0, 1]$

LaTeX
T = [T_{ij}]_{m \times n},\ T_{ij} = \{\sigma_{ij} e^{2\pi i \tau_{ij}},\ \varpi_{ij} e^{2\pi i \Re_{ij}}\};\ w = (w_1, \ldots, w_n),\ \sum w_j = 1;\ \Upsilon \in [0, 1]
CFZN karar matrisini yön-farkındalıklı σ, τ, ϖ, R bileşenleri başına normalize et Shahid §4 Adım 3 denk 5-6'ya göre.

$T_{i j}^{'} = {\begin{matrix} T_{i j} / {max}_{i} T_{i j}, & j \in B \\ T_{i j} / {min}_{i} T_{i j}, & j \in C \end{matrix} (component-wise on each of σ, τ, ϖ, ℜ)$

LaTeX
T'_{ij} = \begin{cases} T_{ij} / \max_i T_{ij}, & j \in B \\ T_{ij} / \min_i T_{ij}, & j \in C \end{cases}\ (\text{component-wise on each of}\ \sigma, \tau, \varpi, \Re)
WSM ağırlıklı normalize matris WSM_ij = T'_ij · w_j (skaler bileşen-başına çarpım) hesapla Shahid §4 Adım 4 denk 7'ye göre.

$W S M_{i j} = T_{i j}^{'} \cdot w_{j} (applied component-wise on σ, τ, ϖ, ℜ)$

LaTeX
WSM_{ij} = T'_{ij} \cdot w_j\ (\text{applied component-wise on}\ \sigma, \tau, \varpi, \Re)
WPM ağırlıklı normalize matris WPM_ij = (T'_ij)^{w_j} (skaler bileşen-başına üstel) hesapla Shahid §4 Adım 4 denk 8'e göre.

$W P M_{i j} = (T_{i j}^{'})^{w_{j}} (applied component-wise on σ, τ, ϖ, ℜ)$

LaTeX
WPM_{ij} = (T'_{ij})^{w_j}\ (\text{applied component-wise on}\ \sigma, \tau, \varpi, \Re)
WSM ağırlıklı matrisi alternatif başına optimallik değeri Ě^WSM_i için kriterler boyunca birleştir (CFZN satır toplamı) Shahid §4 Adım 5 denk 9'a göre.

${\overset{˘}{E}}_{i}^{W S M} = \sum_{j = 1}^{n} T_{i j}^{'} \cdot w_{j} (component-wise sum across criteria on σ, τ, ϖ, ℜ)$

LaTeX
\breve{E}^{WSM}_i = \sum_{j=1}^{n} T'_{ij} \cdot w_j\ (\text{component-wise sum across criteria on}\ \sigma, \tau, \varpi, \Re)
WPM ağırlıklı matrisi alternatif başına optimallik değeri Ě^WPM_i için kriterler boyunca birleştir (CFZN satır çarpımı) Shahid §4 Adım 5 denk 10'a göre.

${\overset{˘}{E}}_{i}^{W P M} = \prod_{j = 1}^{n} (T_{i j}^{'})^{w_{j}} (component-wise product across criteria on σ, τ, ϖ, ℜ)$

LaTeX
\breve{E}^{WPM}_i = \prod_{j=1}^{n} (T'_{ij})^{w_j}\ (\text{component-wise product across criteria on}\ \sigma, \tau, \varpi, \Re)
Hibrit WASPAS birleştirmesi Ě^WASPAS_i = ϒ·Ě^WSM_i + (1-ϒ)·Ě^WPM_i Shahid §4 Adım 6 denk 11'e göre; paper-default ϒ=1 saf WSM'ye indirgenir.

${\overset{˘}{E}}_{i}^{W A S P A S} = Υ \cdot {\overset{˘}{E}}_{i}^{W S M} + (1 - Υ) \cdot {\overset{˘}{E}}_{i}^{W P M} (component-wise on σ, τ, ϖ, ℜ)$

LaTeX
\breve{E}^{WASPAS}_i = \Upsilon \cdot \breve{E}^{WSM}_i + (1 - \Upsilon) \cdot \breve{E}^{WPM}_i\ (\text{component-wise on}\ \sigma, \tau, \varpi, \Re)
Ě^WASPAS_i'yi CFZN skor fonksiyonu μ = (σ·ϖ + τ·R)/2 Shahid §3 denk 3 ile skalarize ederek skaler skor üret.

$S_{i} = μ ({\overset{˘}{E}}_{i}^{W A S P A S}) = \frac{σ_{i} \cdot ϖ_{i} + τ_{i} \cdot ℜ_{i}}{2}$

LaTeX
S_i = \mu(\breve{E}^{WASPAS}_i) = \frac{\sigma_i \cdot \varpi_i + \tau_i \cdot \Re_i}{2}
Alternatifleri skaler skor S_i'ye göre azalan sırala; en büyük en iyidir Shahid §4 Adım 7'ye göre.

${rank}_{i} = {argsort}_{desc} (S_{i})$

LaTeX
\text{rank}_i = \text{argsort}_\text{desc}(S_i)

Sezgi

Sonucu okuma: CFZN-WASPAS ranks alternatives based on performance scores. Higher score = better rank.

Sık yapılan hatalar

Shahid 2026 paper text OMITS explicit criterion weight values W_ℛ - engine MUST require user-supplied weights and surface a paper-incompleteness warning.
Paper §4 Step 6 sets ϒ=1, reducing WASPAS to pure WSM. Standard WASPAS convention uses ϒ=0.5; document this paper-specific choice and expose ϒ as user parameter.
WSM Table 5 phase values (τ_WSM up to 1.35) exceed paper's own §2.6 constraint τ ∈ [0,1]. This is the natural consequence of summing weighted phases without normalization - paper does not address this constraint violation; engine should warn when post-aggregation τ or R > 1.
WSM scalar component-wise weighting (T'·W applied independently on σ, τ, ϖ, R) is methodologically simplified vs full CFZN ⊗ operator from §3 eq 7 (which would couple σ and τ through complex multiplication). Paper choice is the simpler 4-real-scalar approach; engine should mirror this.
Normalization in Step 3 (eq 5-6) divides each CFZN component (σ, τ, ϖ, R) by per-column max (benefit) or min (cost) independently. This does NOT preserve CFZN constraint τ ∈ [0,1] when original values already at boundary; engine should clip post-normalization to [0,1] with warning.
Score function μ = (σϖ + τR)/2 (Shahid §3 eq 3) couples amplitude pair and phase pair multiplicatively. This is the load-bearing scalarization - μ(Ě^WSM) reproduces Table 7 scores exactly even when phase values > 1.
Both WASPAS (this manifest) and MARCOS (CFZN-MARCOS) share Table 1 input but produce different rankings: WASPAS U2≻U4≻U3≻U1 vs MARCOS U2≻U1≻U4≻U3. U2 is consistently top; ranks 2-4 differ between methods.
Ranking criterion: largest S_i wins. Engine must descending-sort.
Engine should NOT scalarize prematurely - all WSM/WPM aggregations stay in CFZN space (4-tuple) until final μ-scoring.