MCDMDecision-makingRankingMath steps

Dual Hesitant Fuzzy extension of TODIM

OriginatorLiu, Y., Tariq, M., Khan, S., Abdullah, S.Year2023Sources1Related methods8

DHF-TODIM (Dual Hesitant Fuzzy extension of TODIM) is a ranking multi-criteria decision-making (MCDM) method introduced by Liu, Y., Tariq, M., Khan, S., Abdullah, S. in 2023. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Key highlights

  • Follows a transparent, reproducible computational procedure that can be audited step by step.
  • Handles multiple criteria of differing scales and units within a single decision matrix.

Intuition

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How it works

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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

Strengths
  • Follows a transparent, reproducible computational procedure that can be audited step by step.
  • Handles multiple criteria of differing scales and units within a single decision matrix.
Limitations
  • Assumes full compensation — a strong score on one criterion can offset a weak score on another.

Common pitfalls

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Sources

  1. 1.
    Liu, Y., Tariq, M., Khan, S., Abdullah, S. (2023). Complex dual hesitant fuzzy TODIM method and their application in Russia–Ukraine war's impact on global economy. Complex & Intelligent Systems

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ScholarGate. (2026, June 2). DHF-TODIM. ScholarGate. https://scholargate.app/decision-making/dhf-todim

Dual Hesitant Fuzzy extension of TODIM | ScholarGate