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Dual Hesitant Fuzzy extension of COPRAS

OriginatorRani, P., Mishra, A. R., Krishankumar, R., Mardani, A., Cavallaro, F., Ravichandran, K. S., Balasubramanian, K.Year2020Sources1Related methods8

DHF-COPRAS (Dual Hesitant Fuzzy extension of COPRAS) is a ranking multi-criteria decision-making (MCDM) method introduced by Rani, P., Mishra, A. R., Krishankumar, R., Mardani, A., Cavallaro, F., Ravichandran, K. S., Balasubramanian, K. in 2020. 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-COPRAS (Rani & Mishra 2020 HF-SWARA-COPRAS lifted to DHFE) is the dual-hesitant extension of COPRAS with integrated SWARA criterion weighting and entropy-based DE weighting. l decision experts each supply a DHFE matrix; DHFWA (Eq.8 lift of Zhu 2012 Eq.4) aggregates them into the AHF-D matrix using crisp DE weights λ_k (Eq.7 HFS-entropy or direct). Each AHF-D cell is defuzzified via the DHFE score s(d)=mean(h)−mean(g) (Zhu 2012 Def. 2) for SWARA ordering; SWARA Eqs.(9)–(11) yield criterion weights w_j. Cost columns are complemented (Zhu 2012 Eq.6 swap h↔g) and benefit/cost aggregates σ_i, v

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.
    Rani, P., Mishra, A. R., Krishankumar, R., Mardani, A., Cavallaro, F., Ravichandran, K. S., Balasubramanian, K. (2020). Hesitant Fuzzy SWARA-Complex Proportional Assessment Approach for Sustainable Supplier Selection (HF-SWARA-COPRAS). Symmetry
    DOI 10.3390/sym12071152

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