## 3 Methodology
### Neutrosophic Axiomatic Design (NAD)
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Criteria** & **CT-1** & **CT-2** & **CT-3** & **CT-4** \\ \hline CT-1 & 1.0000 & 2.8284 & 3.8730 & 5.9161 \\ \hline CT-2 & 0.3536 & 1.0000 & 2.8284 & 5.9161 \\ \hline CT-3 & 0.2582 & 0.3536 & 1.0000 & 2.8284 \\ \hline CT-4 & 0.1690 & 0.1690 & 0.3536 & 1.0000 \\ \hline \(SUM\) & 1.7808 & 4.3510 & 8.0550 & 15.6606 \\ \hline
**Criteria** & **CT-11** & **CT-12** & **CT-13** & \\ \hline CT-1-1 & 1.0000 & 5.9161 & 8.4853 & \\ \hline CT-1-2 & 0.1690 & 1.0000 & 3.8730 & \\ \hline CT-1-3 & 0.1179 & 0.2582 & 1.0000 & \\ \hline \(SUM\) & 1.2869 & 7.1743 & 13.3583 & \\ \hline
**Criteria** & **CT-21** & **CT-22** & **CT-23** & \\ \hline CT-2-1 & 1.0000 & 3.8730 & 6.9282 & \\ \hline CT-2-2 & 0.2582 & 1.0000 & 3.8730 & \\ \hline CT-2-3 & 0.1443 & 0.2582 & 1.0000 & \\ \hline \(SUM\) & 1.4025 & 5.1312 & 11.8012 & \\ \hline
**Criteria** & **CT-31** & **CT-32** & **CT-33** & \\ \hline CT-31 & 1.0000 & 2.8284 & 6.9282 & \\ \hline CT-32 & 0.3536 & 1.0000 & 5.9161 & \\ \hline CT-33 & 0.1443 & 0.1690 & 1.0000 & \\ \hline \(SUM\) & 1.4979 & 3.9975 & 13.8443 & \\ \hline
**Criteria** & **CT-41** & **CT-42** & **CT-43** & \\ \hline CT-41 & 1.0000 & 6.9282 & 7.9373 & \\ \hline CT-42 & 0.1443 & 1.0000 & 2.8284 & \\ \hline CT-43 & 0.1260 & 0.3536 & 1.0000 & \\ \hline \(SUM\) & 1.2703 & 8.2818 & 11.7657 & \\ \hline \hline \end{tabular} Notation: Authors’ calculation.  
\end{table} 
Table 6: Main criterion and sub-criteria of non-fuzzy comparison matrix. \[ \begin{bmatrix}1&2.8284&3.8730&5.9161\\ 0.3536&1&2.8284&5.9161\\ 0.2041&0.3536&1&2.8284\\ 0.1690&0.1690&0.3536&1\end{bmatrix} \times \begin{bmatrix}0.5176\\ 0.2893\\ 0.1328\\ 0.0604\\ \end{bmatrix} = \begin{bmatrix}2.2072\\ 1.2049\\ 0.5394\\ 0.2437\\ \end{bmatrix} \] \[ \begin{bmatrix}1&5.9161&8.8453\\ 0.1179&0.2582&1\\ \end{bmatrix} \times \begin{bmatrix}0.7456\\ 0.1869\\ 0.0675\\ \end{bmatrix} = \begin{bmatrix}2.4238\\ 0.5742\\ 3.0727\\ 3.0174\\ \end{bmatrix} \] \[ \begin{bmatrix}1&3.8730&6.9282\\ 0.2582&1\\ \end{bmatrix} \times \begin{bmatrix}0.6850\\ 0.2357\\ 0.0793\\ \end{bmatrix} = \begin{bmatrix}2.1475\\ 0.7198\\ 0.2391\\ \end{bmatrix} \] \[ \begin{bmatrix}1&2.8284&6.9282\\ 0.3536&1&5.9161\\ 0.1443&0.3536&1\end{bmatrix} \times \begin{bmatrix}0.6252\\ 0.3045\\ 0.0703\\ \end{bmatrix} = \begin{bmatrix}1.9735\\ 0.9414\\ 0.2120\\ \end{bmatrix} \] \[ \begin{bmatrix}1&6.9282&7.9373\\ 0.1260&0.3536&1\end{bmatrix} \times \begin{bmatrix}0.7661\\ 0.1583\\ 0.0756\\ \end{bmatrix} = \begin{bmatrix}2.4628\\ 0.4827\\ 3.0163\\ \end{bmatrix} \] \[ \begin{bmatrix}2.4628\\ 0.4827\\ 0.2281\\ \end{bmatrix} / \begin{bmatrix}0.7661\\ 0.1583\\ 0.0756\\ \end{bmatrix} = \begin{bmatrix}3.2146\\ 3.0503\\ 3.0160\\ \end{bmatrix} \]  
The calculation of \(\lambda^{max}\) determines the consistency and stability of the decision-making process. For the main system matrix, \(4\times 4\), where \(n=4\), \(\lambda^{max}=4.1324\), reflecting the overall system consistency. For the submatrices, \(3\times 3\), where \(n=3\), the results are: \(\lambda^{max}_{\text{Economic and policy}}=3.1136\), \(\lambda^{max}_{\text{Environmental}}=3.0675\), \(\lambda^{max}_{\text{social}}=3.0880\), and \(\lambda^{max}_{\text{Technical and operational}}=3.0937\). These values, close to their respective \(n\), confirm the reliability of judgments across all criteria, supporting a stable and consistent decision-making framework. \[ \begin{array}{l}\lambda^{max}_{main}=\frac{4.2647+4.1649+0.0636+4.0362}{4}=4.1324\\ \lambda^{max}_{\text{Economic and policy}}=\frac{3.2507+3.0727+3.0174}{3}=3.1136 \\ \lambda^{max}_{\text{Environmental}}=\frac{3.1352+3.0536+3.0136}{3}=3.0675\\ \lambda^{max}_{\text{social}}=\frac{3.156+3.0916+3.0160}{3}=3.0880\\ \lambda^{max}_{\text{Technical and operational}}=\frac{3.2146+3.0503+3.0163}{3}=3.0937\end{array} \]  
The consistency index (CI) and consistency ratio (CR) are calculated to assess the reliability of pairwise comparisons in the decision-making process.