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Home›Decision-making›Hesitant Fuzzy TODIM via new measure function Z_δ (Zhang-Xu 2016 ITOR)
MCDMRankinghesitant

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

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.

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HF-TODIM
AHPANPBWMBWM-BAYESIANCCSDCILOSCIMASCRITIC

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.

Sources

  1. Zhang, Y., Xu, Z. (2016). Efficiency evaluation of sustainable water management using the HF-TODIM method. International Transactions in Operational Research DOI: 10.1111/itor.12318 ↗

How to cite this page

ScholarGate. (2026, June 2). Hesitant Fuzzy TODIM via new measure function Z_δ (Zhang-Xu 2016 ITOR). ScholarGate. https://scholargate.app/en/decision-making/hf-todim

Related methods

AHPANPBWMBWM-BAYESIANCCSDCILOSCIMASCRITIC

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Similar methods

HF-TOPSISHF-QUALIFLEXDHF-TODIMHF-VIKORHF-SAWHF-CODASPHF-VIKORPF-TODIM

Related reference concepts

Decision MakingDecision Support SystemsCriteria for Decision-Making under Risk and UncertaintyDecision Theory and UtilityDecision Making SkillsWeighted Scores

Spotted an issue on this page? Report or suggest a fix →

ScholarGate — HF-TODIM (Hesitant Fuzzy TODIM via new measure function Z_δ (Zhang-Xu 2016 ITOR)). Retrieved 2026-07-21 from https://scholargate.app/en/decision-making/hf-todim · Dataset: https://doi.org/10.5281/zenodo.20539026
Quick facts
Originator
Zhang, Y., Xu, Z.
Subfamily
Ranking
Year
2016
Type
Prospect-theory pairwise dominance (Gomes-Lima 1992) extended to Hesitant Fuzzy Elements (HFE ⊂ [0,1]) via the parametric Z δ measure function (Zhang-Xu 2016)
Value Space
hesitant
Uncertainty
epistemic
Compensation
partial
Rank Reversal
Yes
Related methods
AHPANPBWMBWM-BAYESIANCCSDCILOSCIMASCRITIC
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