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Ranking
HF-EDAS - Hesitant Fuzzy EDAS (Evaluation Based on Distance from Average Solution)
Hesitant outranking/ranking - Triangular Fuzzy Hesitant Fuzzy Set (TFHFS, Yu 2014): each cell is a finite set of triangular fuzzy numbers in [0,1]^3
Kutlu Gündoğdu, F., Kahraman, C., Civan, H. N.2018doi:10.3233/JIFS-181172 ↗
Overview
HF-EDAS evaluates alternatives by their distance from the average solution under triangular fuzzy hesitant uncertainty. Higher Appraisal Score (AS ∈ [0,1]) indicates an alternative that exceeds the average in benefit criteria and stays below it in cost criteria. For group decisions, aggregate DM evaluations first via TFHFWA/TFHFWG with DM importance weights. Method 1 (defuzz-then-EDAS) is recommended for first-time users; Method 2 (fuzzy-throughout) preserves uncertainty granularity for sensitivity analysis.
- Output
- utility, higher is better
- Data
- Triangular Fuzzy Hesitant, tfhfs complete
- Weights
- Needs a weight source
- Size
- 2+ alternatives, 3-12 criteria works best
- Used for
- Hospital selection (paper application), Supplier selection under linguistic uncertainty, MAGDM with TFN linguistic scales, Healthcare resource allocation
How it works
- 1
Her DM_k için kararsız TFHFS matrisi x̃_ij^(k) topla. TFHFWA Eq.8 ile DM agregasyonu: x̃_ij = ⊕_k w_k · x̃_ij^(k) (TFN-arithmetic). Sonuç: tek bir grup-aggregated TFHFS matrisi.
- 2
Her kriter j için AV_j = TFHFWA(x̃_·j, uniform 1/m) (Eq.32). Yani AV = alternatifler üzerinde tek-tip ağırlıklı TFHFWA. Defuzz def(L,M,U) = (L+4M+U)/6 (Eq.10).
- 3
Method 1 (paper Eq.34-35 default): pdã_ij = ψ_j(x̃_ij ⊖ av̄_j) / def(av̄_j); ndã_ij = ψ_j(av̄_j ⊖ x̃_ij) / def(av̄_j). ψ_j benefit kriter için max(0,·) wrap, cost kriter için yön çevir. Numerator TFN-valued (fuzzy subtraction), denominator crisp.
- 4
SP_i = Σ_j w_j · def(pdã_ij); SN_i = Σ_j w_j · def(ndã_ij). w_j paper Tablo 13 'normalized weight' veya kullanıcı simplex.
- 5
NSP_i = SP_i / max_k(SP_k); NSN_i = 1 − SN_i / max_k(SN_k). Her iki normalize ∈ [0,1].
- 6
AS_i = ½(NSP_i + NSN_i). Final ranking: AS azalan sırada.
Fits when / Look elsewhere when
Fits when
- •AV-based reference (not ideal/anti-ideal) - robust under outlier alternatives compared to TOPSIS
- •Native group-decision via TFHFWA/TFHFWG - no separate DM-aggregation preprocessing required
- •4 internal versions (TFHFWA/TFHFWG × Method 1/2) enable sensitivity check; paper §5.1 reports Hospital B winner invariant across all 4 - strong robustness signal
- •Computational cost lightweight (no LP, no Monte Carlo) - scales O(m·n·|DMs|)
- •Single AS scalar per alternative + descending rank - intuitive output for stakeholders
Look elsewhere when
- •Crisp data sufficient - use base EDAS directly
- •Uncertainty better captured as intuitionistic/picture/spherical fuzzy - use respective variants
- •Non-compensatory decision required - use ELECTRE or PROMETHEE family
Assumptions to verify
- Decision matrix entries are valid TFHFS (sets of TFNs in [0,1]^3 with L≤M≤U)
- Criterion compensation (additive trade-offs) is acceptable
- All DMs use the same linguistic-to-TFN scale
- Weights are externally provided (subjective, objective, or hybrid)
Limitations
- •Strong dependence on AV - if alternatives are highly skewed, AV may not be a meaningful reference
- •Method 1 (defuzz-based) loses TFN spread information at PDA/NDA stage; Method 2 (TFN-arithmetic) preserves but adds implementation complexity
- •TFHFS value-space is restrictive - does not natively handle scalar HFS (Torra 2010) or linguistic EHFLTS
- •Compensation between PDA and NDA (½(NSP+NSN) symmetric weighting) is hard-coded; cannot weight benefit-side vs cost-side asymmetrically
- •Tie-breaking is by deterministic argsort on alternative_id - paper does not specify a principled tiebreaker
Edge cases and pitfalls
- •max(SP_k)=0 → tüm NSP_i=0, AS sadece NSN'den (EC-1)
- •max(SN_k)=0 → tüm NSN_i=1, AS sadece NSP'den (EC-2)
- •Cardinality >1 TFHFS hücreleri = çoklu uzman TFN'leri → TFHFWA agregasyonu DM-uniform veya kullanıcı weights (EC-4)
- •L=M=U degenerate TFN → crisp EDAS davranışına geri düşer (EC-6)
- •Method 2 (Φ sign) seçilirse TFN-aware arithmetic library zorunlu; scalar fallback sessiz hata üretir (EC-5)
Confusing TFHFS (triangular fuzzy hesitant, Yu 2014) with classic HFS (Torra 2010): TFHFS cells are sets of TFNs (each a triple), not scalars. Implementations must not pass Torra HFS directly into TFHFWA.
Picking Method 2 (fuzzy-throughout) without TFHFS-aware SP/SN normalisation logic produces incorrect rankings; Method 1 is the safer default when validation tooling for fuzzy SP/SN is unavailable.
Treating cost criteria as benefit (or vice versa) inverts PDA/NDA computation and yields inverted rankings.
When max(SP)=0 (no alternative exceeds AV on any benefit criterion) or max(SN)=0, normalization division-by-zero must be handled (default: NSP=0 / NSN=1 respectively).
Works with
How to cite
Kutlu Gündoğdu, F.; Kahraman, C.; Civan, H. N. (2018). A novel hesitant fuzzy EDAS method and its application to hospital selection. Journal of Intelligent & Fuzzy Systems. https://doi.org/10.3233/JIFS-181172
System ID, as it appears in reports and the API
HF-EDAS