MCDMDecision-makingRankingMath steps

Hesitant Fuzzy TODIM via new measure function Z_δ (Zhang-Xu 2016 ITOR)

OriginatorZhang, Y., Xu, Z.Year2016Sources1Related methods8

HF-TODIM (Hesitant Fuzzy TODIM via new measure function Z_δ (Zhang-Xu 2016 ITOR)) is a ranking multi-criteria decision-making (MCDM) method introduced by Zhang, Y., Xu, Z. in 2016. 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

Φ ∈ [0,1] is the overall prospect value: 1 = best alternative under min-max normalisation, 0 = worst. Φ is NOT a probability or utility; it is a normalised aggregate of pairwise loss-averse dominance. Always report δ and θ alongside the ranking — different (δ, θ) pairs can produce different rankings on the same data (Zhang-Xu 2016 §5 'different methods of extension could produce different results'). For benchmark fidelity to the paper use δ=1, θ=1, risk_averse extension.

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
  • May exhibit rank reversal when alternatives are added to or removed from the set.

Common pitfalls

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Sources

  1. 1.
    Zhang, Y., Xu, Z. (2016). Efficiency evaluation of sustainable water management using the HF-TODIM method. International Transactions in Operational Research

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

Hesitant Fuzzy TODIM via new measure function Z_δ (Zhang-Xu 2016 ITOR)