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

Name: DecisionMind
Author: SciMind

1. 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).
$S c (E_{h}) = (m u_{h} + (1 - e t a_{h}) + (1 - n u_{h})) /3; w_{h} = S c (E_{h}) / s u m_{k} S c (E_{k})$
2. 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.
$Z_{hj} = (m u_{hj} + (1 - e t a_{hj}) + (1 - n u_{hj})) /3$
3. Column-sum normalisation across experts: Ỹ_{hj} = Z_{hj} / Σ_h Z_{hj}. Each column sums to 1.
$Y_{n} or m_{hj} = Z_{hj} / s u m_{h} Z_{hj}$
4. Expert-weighted matrix L_{hj} = Ỹ_{hj} · w_h.
$L_{hj} = Y_{n} or m_{hj} * w_{h}$
5. 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.
$Y_{j} = ma x_{h} L_{hj}; X_{j} = mi n_{h} L_{hj}; B_{j} = Y_{j} - X_{j}; w_{j} = B_{j} / s u m_{j} B_{j}$
6. 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.
$R I = s u m_{j} ∣ w_{j} * 100 - w_{j}^{(2 r)} * 100∣/100 (r e q u i r esseco n d - r o u n d w_{j}^{(2 r)})$

1. 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).