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Hybrid

PIF-CIMAS-ARTASI - Hybrid Picture Fuzzy weighting (CIMAS) + ranking (ARTASI)

Two-stage MAGDM: PIF-CIMAS criterion weights → PIF-ARTASI alternative ranking

Kara, K., Yalçın, G. C., Kaygısız, E. G., Simic, V., Örnek, A. Ş., Pamucar, D.2024doi:10.1016/j.asoc.2024.111826 ↗

Overview

Two-stage MAGDM hybrid: stage 1 = PIF-CIMAS computes criterion weights from expert assessments; stage 2 = PIF-ARTASI ranks alternatives. The reliability index RI from stage 1 must be < 0.1 before proceeding.

Output: utility, higher is better
Data: Picture Fuzzy, uncertainty tuples complete
Weights: Needs a weight source
Size: 2+ alternatives, 3-10 criteria works best
Used for: Picture Fuzzy MCDM, MAGDM under epistemic uncertainty, expert-driven evaluation with linguistic terms

How it works

1
Stage 1 (PIF-CIMAS, Steps 1-11): Given expert importance PFS E_h and per-(expert,criterion) PFS Z̃_{hj}: Sc(E_h) → w_h ; Z_{hj} = Sc(Z̃_{hj}) ; Ỹ_{hj} = Z_{hj}/Σ_h Z_{hj} ; L_{hj} = Ỹ_{hj}·w_h ; B_j = max_h L_{hj} − min_h L_{hj} ; w_j = B_j/Σ_j B_j ; second-round RI check (RI < 0.1).
$S c (p) = (m u + 1 - e t a + 1 - n u) /3; w_{h} = S c (E_{h}) / s u m S c (E_{k}); Z_{hj} = S c (\tilde{Z}_{hj}); Y_{hj} = Z_{hj} / s u m_{h} Z_{hj}; L_{hj} = Y_{hj} * w_{h}; B_{j} = ma xL - min L; w_{j} = B_{j} / s u m B$
Kara et al. 2024, §2.2 Steps 1-11 (Eqs 5-14)
2
Stage 2 (PIF-ARTASI, Steps 12-20): Given per-expert PFS decision matrices W̃^{(h)} and criterion weights w_j from Stage 1: PFWA aggregate (Wang 2017) → U=Sc(W̃) → adaptive bounds (S^max, S^min) → two-level standardization (R, C with β^l=1, β^u=100) → V^+, V^- (Tatar 2025 reversal-on-cost-only) → N^+, N^- → K_i = (N^+ + N^-)·[ψ·N^+τ + (1−ψ)·N^-τ]^{1/τ}; defaults ψ=0.5, τ=1.
$see P I F - A R T A S I F . s t e p s F 1 - F 9; w e i g h t s w_{j} co n s u m e df r o m S t a g e 1$
Kara et al. 2024, §2.2 Steps 12-20 (Eqs 15-26); Tatar 2025 corrections

Fits when / Look elsewhere when

Fits when

•Preserves picture uncertainty through the pipeline rather than premature crispification at elicitation
•Native group-decision support (multi-DM aggregation built into the pipeline)

Look elsewhere when

•Crisp data sufficient - use base CIMAS-ARTASI directly (avoid unnecessary uncertainty layer)
•Aggregation operator (PFWA/PFOWA/etc.) not specified - output ambiguous

Assumptions to verify

Decision matrix entries are valid Picture 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

Edge cases and pitfalls

Skipping the RI check (Stage 1) lets unreliable expert assessments propagate.
Qualitative/quantitative split must match paper convention (PFS for qualitative only).

Works with

Commonly takes its weights from

n_a

How to cite

Kara, K.; Yalçın, G. C.; Kaygısız, E. G.; Simic, V.; Örnek, A. Ş.; Pamucar, D. (2024). A picture fuzzy CIMAS-ARTASI model for website performance analysis in human resource management. Applied Soft Computing. https://doi.org/10.1016/j.asoc.2024.111826

BibTeX RIS APA (.txt)DOI ↗

System ID, as it appears in reports and the API

PIF-CIMAS-ARTASI

Overview

Output

utility, higher is better

Data

Picture Fuzzy, uncertainty tuples complete

Weights

Needs a weight source

Size

2+ alternatives, 3-10 criteria works best

Used for

Picture Fuzzy MCDM, MAGDM under epistemic uncertainty, expert-driven evaluation with linguistic terms

How it works

Stage 1 (PIF-CIMAS, Steps 1-11): Given expert importance PFS E_h and per-(expert,criterion) PFS Z̃_{hj}: Sc(E_h) → w_h ; Z_{hj} = Sc(Z̃_{hj}) ; Ỹ_{hj} = Z_{hj}/Σ_h Z_{hj} ; L_{hj} = Ỹ_{hj}·w_h ; B_j = max_h L_{hj} − min_h L_{hj} ; w_j = B_j/Σ_j B_j ; second-round RI check (RI < 0.1).

S c (p) = (m u + 1 - e t a + 1 - n u) /3; w_{h} = S c (E_{h}) / s u m S c (E_{k}); Z_{hj} = S c (\tilde{Z}_{hj}); Y_{hj} = Z_{hj} / s u m_{h} Z_{hj}; L_{hj} = Y_{hj} * w_{h}; B_{j} = ma xL - min L; w_{j} = B_{j} / s u m B

Kara et al. 2024, §2.2 Steps 1-11 (Eqs 5-14)

Stage 2 (PIF-ARTASI, Steps 12-20): Given per-expert PFS decision matrices W̃^{(h)} and criterion weights w_j from Stage 1: PFWA aggregate (Wang 2017) → U=Sc(W̃) → adaptive bounds (S^max, S^min) → two-level standardization (R, C with β^l=1, β^u=100) → V^+, V^- (Tatar 2025 reversal-on-cost-only) → N^+, N^- → K_i = (N^+ + N^-)·[ψ·N^+τ + (1−ψ)·N^-τ]^{1/τ}; defaults ψ=0.5, τ=1.

see P I F - A R T A S I F . s t e p s F 1 - F 9; w e i g h t s w_{j} co n s u m e df r o m S t a g e 1

Kara et al. 2024, §2.2 Steps 12-20 (Eqs 15-26); Tatar 2025 corrections