N-EDAS: Neutrosophic extension of EDAS

Overview

Neutrosophic outranking/ranking: Single-Valued Neutrosophic Set (SVNS: T, I, F; T,I,F ∈ [0,1], T+I+F ≤ 3). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Neutrosophic outranking/ranking: Single-Valued Neutrosophic Set (SVNS: T, I, F; T,I,F ∈ [0,1], T+I+F ≤ 3)
• •Preserves single_valued_neutrosophic uncertainty through the pipeline rather than premature crispification at elicitation
• •Native group-decision support (multi-DM aggregation built into the pipeline)

Limitations

• •Rank reversal known on alternative-set changes (ref: inherited from crisp base; cf. Belton-Gear 1983, Wang-Luo 2009)
• •Assumes: Decision matrix entries are valid Single-Valued Neutrosophic numbers/tuples
• •Assumes: Underlying crisp method's compensation assumption holds in uncertain space
• •Assumes: All decision-maker(s) and experts use the same linguistic/uncertainty scale

Assumptions to verify

• •Decision matrix entries are valid Single-Valued Neutrosophic numbers/tuples
• •Underlying crisp method's compensation assumption holds in uncertain space
• •All decision-maker(s) and experts use the same linguistic/uncertainty scale

When not to use

• •Crisp data sufficient: use base EDAS directly (avoid unnecessary uncertainty layer)
• •Aggregation operator (PFWA/PFOWA/etc.) not specified: output ambiguous

Edge cases

• •See F.steps and D.parameters for N-EDAS-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

• •Hatalı: 'N-EDAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix entries are valid Single-Valued Neutrosophic numbers/tuples
• •Hatalı: 'N-EDAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Underlying crisp method's compensation assumption holds in uncertain space
• •Hatalı: 'N-EDAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All decision-maker(s) and experts use the same linguistic/uncertainty scale
• •Hatalı: N-EDAS'yi 'Crisp data sufficient' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: N-EDAS'yi 'Aggregation operator (PFWA/PFOWA/etc.) not specified' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): SVN decision matrix construction. Formül: \mathbf{D}=(\langle T_{ij},I_{ij},F_{ij}\rangle)_{m\times n};\quad s(\alpha)=\tfrac{1+T-2I-F}{2} Anchor: Stanujkić et al. 2021 Axioms, Sec.3 Step1
2. 2.Adım 2 (F2): SVN average solution: component-wise arithmetic mean. Formül: \overline{\alpha}_j=\Bigl\langle\tfrac{1}{m}\sum_i T_{ij},\;\tfrac{1}{m}\sum_i I_{ij},\;\tfrac{1}{m}\sum_i F_{ij}\Bigr\rangle Anchor: Stanujkić et al. 2021 Axioms, Sec.3 Step2
3. 3.Adım 3 (F3): PDA and NDA: signed neutrosophic distances from average. Formül: d(\alpha,\overline{\alpha}_j)=\sqrt{\tfrac{(T-\bar{T}_j)^2+(I-\bar{I}_j)^2+(F-\bar{F}_j)^2}{3}};\quad d_j^{\max}=\max_k d(\tilde{a}_{kj},\overline{\alpha}_j);\quad\mathrm{PDA}_{ij}=\max(0,\;d_{ij}\cdot\mathbf{1}[s(\tilde{a}_{ij})>s(\overline{\alpha}_j)])/d_j^{\max};\quad\mathrm{NDA}_{ij}=\max(0,\;d_{ij}\cdot\mathbf{1}[s(\tilde{a}_{ij})<s(\overline{\alpha}_j)])/d_j^{\max} Anchor: Stanujkić et al. 2021 Axioms, Sec.3 Step3
4. 4.Adım 4 (F4): Weighted sums SP_i and SN_i; reverse for cost criteria. Formül: SP_i=\sum_j w_j\mathrm{PDA}_{ij};\quad SN_i=\sum_j w_j\mathrm{NDA}_{ij} Anchor: Stanujkić et al. 2021 Axioms, Sec.3 Step4
5. 5.Adım 5 (F5): Normalise SP and SN. Formül: NSP_i=\frac{SP_i}{\max_k SP_k};\quad NSN_i=1-\frac{SN_i}{\max_k SN_k} Anchor: Stanujkić et al. 2021 Axioms, Sec.3 Step5
6. 6.Adım 6 (F6): Appraisal score; rank descending. Formül: AS_i=\tfrac{1}{2}(NSP_i+NSN_i);\quad AS_i\in[0,1];\quad\text{rank descending} Anchor: Stanujkić et al. 2021 Axioms, Sec.3 Step6-7

Commonly paired with

• •n_a + N-EDAS (common)

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