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DEA
HFEA - Hesitant Fuzzy Envelopment Analysis (DHFEA / SHFEA, Zhou-Chen-Xu-Meng 2018)
DEA extension to Hesitant Fuzzy Sets - efficiency measured as weighted score-to-deviation ratio m_e = Σp_i·s_{ie} / Σq_i·d_{ie}; LP-solved in linearised DHFEA (deviation-normalised) or SHFEA (score-normalised) form; provides both ranking and improvement schedules for inefficient alternatives.
Zhou, W., Chen, J., Xu, Z. S., Meng, S.2018doi:10.1016/j.ins.2018.07.002 ↗
Overview
Efficiency score m_e = 1 means the alternative lies on the HFS efficient frontier (cannot be improved given the current set). Scores below 1 indicate how far the alternative is from the frontier. The improvement schedules (Block G: improvement_schedule_scores / deviations) show the minimum required score increases and deviation decreases to become efficient.
- Data
- Hesitant
Edge cases and pitfalls
Treating all criteria as benefit-type without pre-converting cost criteria via complement (1 - h).
Using fewer alternatives than criteria (K ≤ n) - leads to all alternatives being efficient (LP trivially satisfied), analogous to DEA's n/3 rule of thumb.
Interpreting tied efficient alternatives (m_e = 1) as identical in quality - switch to HFPE/HFGPE for full discrimination.
Works with
How to cite
Zhou, W.; Chen, J.; Xu, Z. S.; Meng, S. (2018). Hesitant fuzzy preference envelopment analysis and alternative improvement. Information Sciences. https://doi.org/10.1016/j.ins.2018.07.002
System ID, as it appears in reports and the API
HFEA