PIF-CIMAS: Picture Fuzzy variant of CIMAS (Kara et al. 2024)

Overview

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

Strengths

• •Method-specific: Picture Fuzzy criteria weighting via expert assessment (CIMAS): PFWA aggregation
• •Preserves picture uncertainty through the pipeline rather than premature crispification at elicitation
• •Native group-decision support (multi-DM aggregation built into the pipeline)

Limitations

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

Assumptions to verify

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

When not to use

• •Crisp pairwise data available: use base CIMAS
• •Experts disagree fundamentally on scale interpretation

Edge cases

• •See F.steps and D.parameters for PIF-CIMAS-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

• •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 'Crisp 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.

Worked example

1. 1.Adım 1 (F1): 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). Formül: Sc(E_h) = (mu_h + (1 - eta_h) + (1 - nu_h)) / 3 ; w_h = Sc(E_h) / sum_k Sc(E_k) Anchor: Kara et al. 2024, Eqs (5)-(6)
2. 2.Adım 2 (F2): 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. Formül: Z_{hj} = (mu_{hj} + (1 - eta_{hj}) + (1 - nu_{hj})) / 3 Anchor: Kara et al. 2024, Eq (7)
3. 3.Adım 3 (F3): Step 6 (Eq 8): Column-sum normalisation across experts: Ỹ_{hj} = Z_{hj} / Σ_h Z_{hj}. Each column sums to 1. Formül: Y_norm_{hj} = Z_{hj} / sum_h Z_{hj} Anchor: Kara et al. 2024, Eq (8)
4. 4.Adım 4 (F4): Step 7 (Eq 9): Expert-weighted matrix L_{hj} = Ỹ_{hj} · w_h. Formül: L_{hj} = Y_norm_{hj} * w_h Anchor: Kara et al. 2024, Eq (9)
5. 5.Adım 5 (F5): 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. Formül: 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 Anchor: Kara et al. 2024, Eqs (10)-(13)
6. 6.Adım 6 (F6): 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. Formül: RI = sum_j |w_j*100 - w_j^{(2r)}*100| / 100 (requires second-round w_j^{(2r)}) Anchor: Kara et al. 2024, Eq (14)

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