PIF-CIMAS - Resim Bulanık CIMAS (Kara ve ark. 2024)

Formül adımları

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

Adım 1-3 (Eqs 5-6): Her uzman PFS önem değerlendirmesi için Sc(E_h) = (μ_h + (1−η_h) + (1−ν_h))/3; sonra w_h = Sc(E_h) / Σ_k Sc(E_k).

$S c (E_{h}) = (m u_{h} + (1 - e t a_{h}) + (1 - n u_{h})) / 3; w_{h} = S c (E_{h}) / s u m_{k} S c (E_{k})$

LaTeX
Sc(E_h) = (mu_h + (1 - eta_h) + (1 - nu_h)) / 3 ; w_h = Sc(E_h) / sum_k Sc(E_k)
Adım 4 (Eq 7): PFS kriter değerlendirme matrisi Z̃_{hj} → kripşik Z_{hj} = Sc(Z̃_{hj}).

$Z_{h j} = (m u_{h j} + (1 - e t a_{h j}) + (1 - n u_{h j})) / 3$

LaTeX
Z_{hj} = (mu_{hj} + (1 - eta_{hj}) + (1 - nu_{hj})) / 3
Adım 6 (Eq 8): Ỹ_{hj} = Z_{hj} / Σ_h Z_{hj}; her kolon 1'e eşit.

$Y_{n} o r m_{h j} = Z_{h j} / s u m_{h} Z_{h j}$

LaTeX
Y_norm_{hj} = Z_{hj} / sum_h Z_{hj}
Adım 7 (Eq 9): L_{hj} = Ỹ_{hj} · w_h.

$L_{h j} = Y_{n} o r m_{h j} * w_{h}$

LaTeX
L_{hj} = Y_norm_{hj} * w_h
Adım 8-10: Y_j = max L_{hj}, X_j = min L_{hj}, B_j = Y_j − X_j, w_j = B_j / Σ B.

$Y_{j} = m a x_{h} L_{h j}; X_{j} = m i n_{h} L_{h j}; B_{j} = Y_{j} - X_{j}; w_{j} = B_{j} / s u m_{j} B_{j}$

LaTeX
Y_j = max_h L_{hj} ; X_j = min_h L_{hj} ; B_j = Y_j - X_j ; w_j = B_j / sum_j B_j
Adım 11 (Eq 14): İkinci tur w_j^{(2r)} ile RI; RI<0.1 koşulu.

$R I = s u m_{j} | w_{j} * 100 - w_{j}^{(2 r)} * 100 | / 100 (r e q u i r e s s e c o n d - r o u n d w_{j}^{(2 r)})$

LaTeX
RI = sum_j |w_j*100 - w_j^{(2r)}*100| / 100 (requires second-round w_j^{(2r)})

Sezgi

Picture Fuzzy criteria weighting via expert assessment (CIMAS) - PFWA aggregation. Output typically weight (higher value = preferred).

Sonucu okuma: PIF-CIMAS extends CIMAS (Bošković et al. 2023) by replacing crisp expert/criterion ratings with Picture Fuzzy linguistic variables aggregated via score function Sc(W) = (1/3)(μ + (1−η) + (1−ν)). Reliability is verified via a second round.

Varsayımlar

Experts can articulate preferences in Picture Fuzzy linguistic variables
Pairwise comparisons satisfy consistency requirements of underlying method

Ne zaman kullanılmaz

Classical pairwise data available - use base CIMAS
Experts disagree fundamentally on scale interpretation

Sınırlılıklar

Assumes: Experts can articulate preferences in Picture Fuzzy linguistic variables
Assumes: Pairwise comparisons satisfy consistency requirements of underlying method

Sık yapılan hatalar

Hatalı: 'PIF-CIMAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Experts can articulate preferences in Picture Fuzzy linguistic variables
Hatalı: 'PIF-CIMAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Pairwise comparisons satisfy consistency requirements of underlying method
Hatalı: PIF-CIMAS'yi 'Classical pairwise data available' durumunda kullanmak - recommendation_metadata.not_recommended_when alternatif öneriyor.
Hatalı: PIF-CIMAS'yi 'Experts disagree fundamentally on scale interpretation' durumunda kullanmak - recommendation_metadata.not_recommended_when alternatif öneriyor.

Hesap adımları ve dayanakları

Steps 1-3 (paper Eqs 5-6): For each expert E_h providing a PFS importance assessment, compute crisp score Sc(E_h) = (μ_h + (1−η_h) + (1−ν_h))/3; then expert weights w_h = Sc(E_h) / Σ_k Sc(E_k).

Dayanak: Kara et al. 2024, Eqs (5)-(6)
Step 4 (Eq 7): Build per-expert per-criterion PFS assessment matrix Z̃_{hj} (h=expert, j=criterion). Compute crisp Z_{hj} = Sc(Z̃_{hj}) = (μ_{hj} + (1−η_{hj}) + (1−ν_{hj}))/3.

Dayanak: Kara et al. 2024, Eq (7)
Step 6 (Eq 8): Column-sum normalisation across experts: Ỹ_{hj} = Z_{hj} / Σ_h Z_{hj}. Each column sums to 1.

Dayanak: Kara et al. 2024, Eq (8)
Step 7 (Eq 9): Expert-weighted matrix L_{hj} = Ỹ_{hj} · w_h.

Dayanak: Kara et al. 2024, Eq (9)
Steps 8-10 (Eqs 10-13): Per criterion j compute Y_j = max_h L_{hj}, X_j = min_h L_{hj}, range B_j = Y_j − X_j (paper's Γ_j), then w_j = B_j / Σ_j B_j.

Dayanak: Kara et al. 2024, Eqs (10)-(13)
Step 11 (Eq 14): After a second elicitation round producing w_j^{(2r)}, compute Reliability Index RI = Σ_j |w_j·100 − w_j^{(2r)}·100| / 100. Require RI < 0.1 for acceptance. Second-round data is not part of the synthetic Block J fixture.

Dayanak: Kara et al. 2024, Eq (14)