## 3 Methodology
### Neutrosophic Axiomatic Design (NAD)
For the main system matrix (\(n=4\), RI = 0.9), CI\({}_{\text{main}}=0.04\) and CR = 4.9%, indicating good consistency. For the submatrices (\(n=3\), RI = 0.58), the results are as follows: CI\({}_{\text{Economic and policy}}=0.06\)and CR = 9.8%; \(\text{CI}_{\text{Environmental}}\) = 0.03 and CR = 5.8%; \(\text{CI}_{\text{social}}\) = 0.04 and CR = 7.6%; \(\text{CI}_{\text{Technical and operational}}\) = 0.05 and CR = 8.1%. Since all CR values are below the acceptable threshold of 10%, the pairwise comparisons demonstrate acceptable consistency, validating the reliability of the evaluation process. \[\text{CI}_{\text{main}}=\frac{\lambda^{\text{max}}-\text{n}}{ \text{n}-1}=\frac{4.1324-4}{3}=0.04\] \[\text{CI}_{\text{Economic and policy}}=\frac{\lambda^{\text{max}}- \text{n}-1}{\text{n}-1}=\frac{3.1136-3}{2}=0.06\] \[\text{CI}_{\text{Environmental}}=\frac{\lambda^{\text{max}}- \text{n}-1}{\text{n}-1}=\frac{3.0675-2}{2}=0.03\] \[\text{CI}_{\text{social}}=\frac{\lambda^{\text{max}}- \text{n}-1}{\text{n}-1}=\frac{3.0880-2}{2}=0.04\] \[\text{CI}_{\text{Technical and operational}}=\frac{\lambda^{\text{max}} -\text{n}-1}{\text{n}-2}=\frac{3.0937-3}{2}=0.05\] \[\text{CR}=\frac{\text{CI}}{\text{RI}}=\frac{0.04}{0.9}=0.0498 \approx 4.9\%\] \[\text{CR}(\text{Economic and policy})=\frac{\text{CI}}{\text{RI}}= \frac{0.06}{0.58}=0.098\approx 9.8\%\] \[\text{CR}(\text{Environmental})=\frac{\text{CI}}{\text{RI}}= \frac{0.03}{0.58}=0.058\approx 5.8\%\] \[\text{CR}(\text{social})=\frac{\text{CI}}{\text{RI}}= \frac{0.04}{0.58}=0.076\approx 7.6\%\] \[\text{CR}(\text{Technical and operational})=\frac{\text{CI}}{\text{RI}}= \frac{0.05}{0.58}=0.081\approx 8.1\%\]  
Based on the aforementioned findings, the pairwise comparison matrix's consistency can be considered acceptable and utilized for additional computations, as indicated by the coefficient of consistency being less than 10%. Other pairwise comparison matrices are performed similarly with this consistency determination procedure. The next step, as shown in Table 8, presents the results of calculating the geometric mean of the four main criteria (CT-1 to CT-4) using the fuzzy geometric mean method. The sum of the main criteria is determined with three components of the triangular fuzzy number, represented by a triplet of values (Lower, Middle, Upper). The inverse of the sum is also calculated to assist in determining the fuzzy weight of each criterion. The geometric mean of the sub-criteria, grouped by each main criterion. Each group of sub-criteria has its own geometric sum and inverse to normalize the weight. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Criteria** & **CT-1** & **CT-2** & **CT-3** & **CT-4** & **Priority Vector** \\ \hline CT-1 & 0.5616 & 0.6501 & 0.4808 & 0.3778 & 0.5176 \\ \hline CT-2 & 0.1985 & 0.2298 & 0.3511 & 0.3778 & 0.2893 \\ \hline CT-3 & 0.1450 & 0.0813 & 0.1241 & 0.1806 & 0.1328 \\ \hline CT-4 & 0.0949 & 0.0388 & 0.0439 & 0.0639 & 0.0604 \\ \hline
**Criteria** & **CT-11** & **CT-12** & **CT-13** & **Priority Vector** \\ \hline CT-11 & 0.7771 & 0.8246 & 0.6352 & 0.7456 \\ \hline CT-12 & 0.1313 & 0.1394 & 0.2899 & 0.1869 \\ \hline CT-13 & 0.0916 & 0.0360 & 0.0749 & 0.0675 \\ \hline
**Criteria** & **CT-21** & **CT-22** & **CT-23** & **Priority Vector** \\ \hline CT-21 & 0.7130 & 0.7548 & 0.5871 & 0.6850 \\ \hline CT-22 & 0.1841 & 0.1949 & 0.3282 & 0.2357 \\ \hline CT-23 & 0.1029 & 0.0503 & 0.0847 & 0.0793 \\ \hline
**Criteria** & **CT-21** & **CT-22** & **CT-23** & **Priority Vector** \\ \hline CT-21 & 0.7130 & 0.7548 & 0.5871 & 0.6252 \\ \hline CT-22 & 0.1841 & 0.1949 & 0.3282 & 0.3045 \\ \hline CT-23 & 0.1029 & 0.0503 & 0.0847 & 0.0703 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Priority vector and normalization comparison matrix as primary criteria and sub-criteria. The fuzzy weight determination process evaluates the importance of criteria and sub-criteria using the ratio of the reciprocal of the geometric mean to the geometric mean.