SFZN-CRITIC - Spherical Fuzzy Z-Number CRITIC Weighting

Overview

Output is an objective weight vector summing to 1 - criteria with high variability AND low correlation with other criteria receive the largest weights. Use these weights downstream in any SFZN-compatible ranking method (SFZN-CRADIS, SFZN-MARCOS, SFZN-TOPSIS). The score function ℑ collapses the SFZN's six components into a single scalar; criteria with discriminating scores AND independent information content dominate.

Data

Spherical Fuzzy Z-Number

Weights

Derived internally, no weight source needed

Edge cases and pitfalls

• Forgetting the §_j multiplier in Γ_j - Niu §III Step 3 writes Γ_j = Σ(1 − Υ_jl) without §_j prefactor, but standard Diakoulaki 1995 CRITIC requires Γ_j = §_j · Σ(1 − Υ_jl); without §_j Niu Table V weights cannot be reproduced from Table IV alone.

• Treating cost criteria as benefit by skipping the direction-aware normalization (Niu §III Step 3 second formula).

• Using m−1 (sample) standard deviation instead of m (population) - Niu §III Step 3 third formula divides by m, not m−1.

Works with

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