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Hesitant Fuzzy TOPSIS with optional incomplete weight information (Xu-Zhang 2013 KBS)

OriginatorXu, Z., Zhang, X.Year2013Sources1Related methods9

HF-TOPSIS (Hesitant Fuzzy TOPSIS with optional incomplete weight information (Xu-Zhang 2013 KBS)) is a ranking multi-criteria decision-making (MCDM) method introduced by Xu, Z., Zhang, X. in 2013. 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

C_i ∈ [0,1] is the closeness coefficient: 1 = identical to PIS on every criterion (best), 0 = identical to NIS (worst). C_i is NOT a probability or utility; it is a normalised distance ratio. Always report the weight_info_mode AND the resolved weights w alongside the ranking — different modes can produce different rankings on the same data (Xu-Zhang 2013 §5 Case 1 vs Case 2 swap A1/A4). For benchmark fidelity to the paper use η=0 (risk-averse) length-equalisation. For η-sensitivity sweep see S.weight_perturbation and T.custom_extensions.

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.
  • 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.
    Xu, Z., Zhang, X. (2013). Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information. Knowledge-Based Systems
    DOI 10.1016/j.knosys.2013.05.011

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