SFZN-CRADIS - Spherical Fuzzy Z-Number CRADIS Ranking

Overview

Output ranks alternatives by Q_i ∈ [0, 1] (compromise score combining utility to ideal and utility to anti-ideal). Best alternative has highest Q. CRADIS uses GLOBAL ideal/anti-ideal anchors (single t+, t- per criterion across all alternatives), distinct from TOPSIS's per-criterion ideal. The best-anchored utility formulation K+ = S°+/S+ and K- = S-/S°- guarantees both K ∈ [0,1] with best alternative receiving K=1 in each - the alternative that wins both K+ AND K- gets Q=1. SFZN reliability (τ_ε, τ_ν, τ_∂) modulates each component via the product (component × reliability) inside the Euclidean distance.

Data

Spherical Fuzzy Z-Number

Weights

Needs a weight source

Edge cases and pitfalls

• Confusing Niu 2024 K+ formula K+_i = S°+/S+_i with Puška 2022 ZF-CRADIS K+_i = S/S+_i where S = average of (S°+, S°-) - the two papers use different normalization references.

• Using TOPSIS per-criterion ideal instead of CRADIS global ideal - CRADIS computes ONE t+ and ONE t- across the entire decision matrix per criterion, then sums distances.

• Forgetting the cost-criterion swap (ε,τ_ε)↔(∂,τ_∂) in F4 normalization - required so the ideal-anchor logic works uniformly across benefit and cost criteria.

• Distance formula uses (ε × τ_ε) products, not separate ε and τ_ε terms - the reliability multiplier collapses each component to a single scalar before the squared difference.

How to cite