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Portfolio
HF-TradeOff-Portfolio - Hesitant Fuzzy Score-Deviation Trade-Off Portfolio Selection (Zhou-Xu 2018)
Hesitant fuzzy portfolio selection for risk-aware investors. Two dual formulations: (A) max-score with deviation upper bound D (Model 3.16) and (B) min-deviation with score lower bound S (Model 3.18). D and S are calibrated per investor risk type (risk-seeker / neutral / risk-averse) via deviation trisection or score trisection approaches (Definitions 3.1-3.2). Generalises HF-MaxScore-Portfolio by incorporating a risk (deviation) constraint.
Zhou, W., Xu, Z.2018
Overview
HF-TradeOff-Portfolio extends HF-MaxScore-Portfolio by enforcing a risk constraint. The deviation trisection automatically calibrates D for three standard investor risk profiles. Score = hesitant fuzzy return; deviation = hesitant fuzzy risk. The efficient frontier (§3.3.2) shows the full score-deviation trade-off curve - useful for visual communication with investors.
- Data
- Hesitant
- Weights
- Derived internally, no weight source needed
Edge cases and pitfalls
min_D=0 occurs when one stock has a single HFE element (zero deviation) - check that this is a genuine investment option, not a degenerate case.
For the neutral investor (D2), the score gain over risk-averse (D3) may be very small - highlight that the return improvement barely compensates the increased risk.
The deviation trisection (Def.3.1) is arbitrary - if investor has specific risk tolerance, use their actual D value instead.
Model 3.18 (min_deviation) and Model 3.16 (max_score) are NOT equivalent - they can give different optimal portfolios for the same risk type.
How to cite
Zhou, W.; Xu, Z. (2018). Portfolio selection and risk investment under the hesitant fuzzy environment. Knowledge-Based Systems.
System ID, as it appears in reports and the API
HF-TRADEOFF-PORT