Dual Hesitant Fuzzy extension of TODIM

When to use it

DHF-TODIM implements the pure-DHFE projection of Liu et al. (2023) CDHF-TODIM. Inputs are Dual Hesitant Fuzzy Elements ρ=(h,g) with γ⁺+η⁺≤1. The 8-step pipeline (F1 input validation; F2 Eq.5.1 cost-complement normalisation; F3 Eq.5.2 relative weights against the heaviest criterion; F4 Eq.3.2 DHFE score; F5 Eq.3.1 DHFE divergence; F6 Eq.5.3 piecewise per-criterion dominance with loss attenuation 1/Φ; F7 Eq.5.5–5.6 cross-criterion aggregation; F8 PI⁺ min–max normalisation and descending sort) carries no probabilistic component and no complex argument. For non-zero complex memberships, use Liu's

Strengths & limitations