N-EDAS - EDAS yönteminin Neutrosophic uzantısı

Formül adımları

Analiz motorunun yöntem bildirimindeki (manifest F.steps) adımlar; raporlardaki formüllerle aynı kaynaktır.

1. SVN decision matrix construction.

   $$𝐃=(⟨T_{ij},I_{ij},F_{ij}⟩{)}_{m\times n};s(\alpha )=\frac{1+T-2I-F}{2}$$
   LaTeX

   \mathbf{D}=(\langle T_{ij},I_{ij},F_{ij}\rangle)_{m\times n};\quad s(\alpha)=\tfrac{1+T-2I-F}{2}

2. SVN average solution: component-wise arithmetic mean.

   $${\bar{\alpha }}_j=\backslash langle\frac{1}{m}\sum _i{T}_{ij},\frac{1}{m}\sum _i{I}_{ij},\frac{1}{m}\sum _i{F}_{ij}\backslash rangle$$
   LaTeX

   \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

3. PDA and NDA: signed neutrosophic distances from average.

   $$d(\alpha ,{\bar{\alpha }}_j)=\sqrt{\frac{(T-{\overline{T}}_j{)}^2+(I-{\overline{I}}_j{)}^2+(F-{\overline{F}}_j{)}^2}{3}};d_j^{max}={max}_{k}d({\tilde{a}}_{kj},{\bar{\alpha }}_j);{\mathrm{P}\mathrm{D}\mathrm{A}}_{ij}=max(0,d_{ij}·\mathbf{1}[s({\tilde{a}}_{ij})>s({\bar{\alpha }}_j)])/d_j^{max};{\mathrm{N}\mathrm{D}\mathrm{A}}_{ij}=max(0,d_{ij}·\mathbf{1}[s({\tilde{a}}_{ij})<s({\bar{\alpha }}_j)])/d_j^{max}$$
   LaTeX

   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}

4. Weighted sums SP_i and SN_i; reverse for cost criteria.

   $$S{P}_i=\sum _j{w}_j{\mathrm{P}\mathrm{D}\mathrm{A}}_{ij};S{N}_i=\sum _j{w}_j{\mathrm{N}\mathrm{D}\mathrm{A}}_{ij}$$
   LaTeX

   SP_i=\sum_j w_j\mathrm{PDA}_{ij};\quad SN_i=\sum_j w_j\mathrm{NDA}_{ij}

5. Normalise SP and SN.

   $$NS{P}_i=\frac{S{P}_i}{{max}_{k}S{P}_k};NS{N}_i=1-\frac{S{N}_i}{{max}_{k}S{N}_k}$$
   LaTeX

   NSP_i=\frac{SP_i}{\max_k SP_k};\quad NSN_i=1-\frac{SN_i}{\max_k SN_k}

6. Appraisal score; rank descending.

   $$A{S}_i=\frac{1}{2}(NS{P}_i+NS{N}_i);A{S}_i\in [0,1];\text{rank descending}$$
   LaTeX

   AS_i=\tfrac{1}{2}(NSP_i+NSN_i);\quad AS_i\in[0,1];\quad\text{rank descending}

Sezgi

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).

Sonucu okuma: n-edas extends EDAS to handle Neutrosophic uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Single-Valued Neutrosophic Set (SVNS: T, I, F; T,I,F ∈ [0,1], T+I+F ≤ 3) algebra. The final scores are defuzzified via score function S = (T − F + 1)/2 before ranking.

Varsayımlar

• 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

Ne zaman kullanılmaz

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

Sınırlılıklar

• 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

Sık yapılan hatalar

• Değer-uzayı ihlali: hesaplamadan önce tüm girişlerin SVNS: T,I,F ∈ [0,1]; 0 ≤ T+I+F ≤ 3 koşulunu sağladığından emin olun.
• Defuzzifikasyon yöntemi sıralamayı etkiler: score function S = (T − F + 1)/2 kanonik seçimdir.