This page is published in English.
Ranking
PHFS-HVaR - Hesitant Value-at-Risk for Probabilistic Hesitant Fuzzy Sets (Zhou-Xu 2017)
Tail decision-making method for probabilistic hesitant fuzzy environments. Input is a PHFE (probabilistic hesitant fuzzy element) - an HFE where each membership value c_l carries an explicit occurrence probability p_l with Σp_l=1. HVaR(h, X) is the boundary membership value at cumulative probability X: the largest c_k such that P(c ≤ c_k) ≥ X. Directly analogous to classical Value-at-Risk (VaR). Intended for risk-averse investors who focus on worst-case outcomes under a given certainty degree.
Zhou, W., Xu, Z.2017doi:10.1016/j.asoc.2017.06.057 ↗
Overview
HVaR is suitable for risk-averse investors who ask 'What is the worst return I can expect under probability X?' A higher HVaR at X=20% means the alternative has a better guaranteed floor. HVaR is simple and intuitive but can produce ties when PHFEs share boundary values. Use EHVaR (PHFS-EHVAR) when discrimination is needed.
- Data
- Probabilistic Hesitant Fuzzy
Edge cases and pitfalls
HVaR is a point estimate (boundary value only) - it ignores all tail information below the boundary. Two very different left tails can have the same HVaR.
Choice of X strongly affects the ranking - always report X alongside HVaR values.
PHFE requires explicit occurrence probabilities; if probabilities are unavailable, use standard HFE with EHVaR not applicable (fall back to HFEA or HF-TOPSIS).
HVaR ranks by loss-tail boundary - this may conflict with overall score ranking (Example 6.2 shows A1 < A2 by score but A1 = A2 by HVaR).
Works with
Its derived weights can feed
How to cite
Zhou, W.; Xu, Z. (2017). Expected hesitant VaR for tail decision making under probabilistic hesitant fuzzy environment. Applied Soft Computing. https://doi.org/10.1016/j.asoc.2017.06.057
System ID, as it appears in reports and the API
PHFS-HVAR