N-CODAS - CODAS yönteminin Neutrosophic uzantısı

Formül adımları

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

1. SVN matrix; cost normalisation via complement.

   $$𝐃=(⟨T_{ij},I_{ij},F_{ij}⟩);\text{cost: }{\widehat{a}}_{ij}=⟨F_{ij},1-I_{ij},T_{ij}⟩;\text{benefit: }{\widehat{a}}_{ij}={\tilde{a}}_{ij}$$
   LaTeX

   \mathbf{D}=(\langle T_{ij},I_{ij},F_{ij}\rangle);\quad\text{cost: }\hat{a}_{ij}=\langle F_{ij},1-I_{ij},T_{ij}\rangle;\quad\text{benefit: }\hat{a}_{ij}=\tilde{a}_{ij}

2. Weighted normalised SVNNs.

   $${\tilde{v}}_{ij}=⟨1-(1-{\widehat{T}}_{ij}{)}^{w_j},{\widehat{I}}_{ij}^{w_j},{\widehat{F}}_{ij}^{w_j}⟩$$
   LaTeX

   \tilde{v}_{ij}=\langle 1-(1-\hat{T}_{ij})^{w_j},\;\hat{I}_{ij}^{w_j},\;\hat{F}_{ij}^{w_j}\rangle

3. Neutrosophic Negative Ideal Solution.

   $${\alpha }_j^{-}=⟨{min}_i{T}_{ij}^v,{max}_i{I}_{ij}^v,{max}_i{F}_{ij}^v⟩$$
   LaTeX

   \alpha_j^-=\langle\min_i T_{ij}^v,\;\max_i I_{ij}^v,\;\max_i F_{ij}^v\rangle

4. Euclidean E_i and Taxicab T_i separations from NIS.

   $$d_E({\alpha }_1,{\alpha }_2)=\sqrt{\frac{(T_1-T_2{)}^2+(I_1-I_2{)}^2+(F_1-F_2{)}^2}{3}};d_H=\frac{|T_1-T_2|+|I_1-I_2|+|F_1-F_2|}{3};E_i=\sqrt{{\sum }_j{w}_j[d_E({\tilde{v}}_{ij},{\alpha }_j^{-}){]}^2};T_i=\sum _j{w}_j{d}_H({\tilde{v}}_{ij},{\alpha }_j^{-})$$
   LaTeX

   d_E(\alpha_1,\alpha_2)=\sqrt{\tfrac{(T_1-T_2)^2+(I_1-I_2)^2+(F_1-F_2)^2}{3}};\quad d_H=\tfrac{|T_1-T_2|+|I_1-I_2|+|F_1-F_2|}{3};\quad E_i=\sqrt{\sum_j w_j[d_E(\tilde{v}_{ij},\alpha_j^-)]^2};\quad T_i=\sum_j w_j d_H(\tilde{v}_{ij},\alpha_j^-)

5. Relative assessment matrix h_ik with threshold τ.

   $$h_{ik}=(E_i-E_k)+\psi (E_i-E_k)·(T_i-T_k);\psi (x)=\{\begin{array}{cc}1\hfill & |x|\ge \tau \hfill \\ 0\hfill & |x|<\tau \hfill \end{array},\tau =0.02$$
   LaTeX

   h_{ik}=(E_i-E_k)+\psi(E_i-E_k)\cdot(T_i-T_k);\quad\psi(x)=\begin{cases}1&|x|\geq\tau\\0&|x|<\tau\end{cases},\;\tau=0.02

6. Appraisal score AS_i; rank descending.

   $$A{S}_i=\sum _{k=1}^m{h}_{ik};\text{rank descending}$$
   LaTeX

   AS_i=\sum_{k=1}^m h_{ik};\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-codas extends CODAS 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 CODAS directly (avoid unnecessary uncertainty layer)
• Aggregation operator (PFWA/PFOWA/etc.) not specified - output ambiguous

Sınırlılıklar

• 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.