## 5 An Innovative Robustness and Reliability Analysis
The SAW method, with the lowest standard deviation, exhibits the least sensitivity and the highest correlation with the constant factor (Entropy-SAW). Conversely, the MCRAT method, with the highest standard deviation, is the most sensitive and shows the lowest correlation with the constant factor. For 2012, the results indicate that FUCA and MCRAT have the highest and lowest averages, respectively. The FUCA method, which has the lowest standard deviation, demonstrates the least sensitivity and the highest correlation with the constant factor, whereas MCRAT has the highest standard deviation. In 2014, FUCA showed the highest averages, while MCRAT had the lowest. The FUCA method was identified as the method with the least sensitivity, whereas MCRAT was the most sensitive. For 2016, FUCA and MCRAT were again identified as having the highest and lowest averages, respectively. FUCA, with a standard deviation of 0.0010, is the method with the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Years** & **MCRAT** & **SAW** & **TOPSIS** & **FUCA** \\ \hline \multirow{3}{*}{2010} & Mean & 0.9794 & 0.9943 & 0.9828 & 0.9928 \\  & StDv & 0.0162 & **0.0039** & 0.0129 & 0.0048 \\  & Mean & 0.9899 & 0.9967 & 0.9902 & 0.9970 \\  & StDv & 0.0106 & 0.0074 & 0.0103 & **0.0018** \\  & Mean & 0.9886 & 0.9968 & 0.9892 & 0.9969 \\  & StDv & 0.0071 & 0.0019 & 0.0068 & **0.0016** \\  & Mean & 0.9926 & 0.9979 & 0.9929 & 0.9978 \\  & StDv & 0.0042 & 0.0011 & 0.0038 & **0.0010** \\  & Mean & 0.9900 & 0.9972 & 0.9896 & 0.9969 \\  & StDv & 0.0064 & **0.0016** & 0.0064 & **0.0016** \\  & Mean & 0.9875 & 0.9964 & 0.9886 & 0.9963 \\  & StDv & 0.0087 & **0.0023** & 0.0076 & **0.0023** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results obtained from the standard deviation of correlations between fixed factors and methods. least sensitivity, while MCRAT remains the most sensitive method. In 2018, TOPSIS had the lowest averages compared to other methods, while SAW had the highest. The SAW and FUCA methods also exhibit the lowest sensitivity (\(\sigma\): 0.0016) and the highest correlation with the constant factor. Finally, for 2023, the SAW method maintained the highest average and MCRAT the lowest, consistent with previous years. The SAW and FUCA methods are identified as the methods with the least sensitivity, while MCRAT remains the most sensitive method. Figure 4 shows how the sensitivity of each method changes among datasets from different years. Here, the FUCA and SAW methods are in a neck-and-neck competition. However, SAW's performance in 2012 does not look good. This shows how the diversity of the dataset affects the sensitivity. Obviously, methodologies may make mistakes in their interpretations when they use a single dataset and a small number of weighting coefficients. We will try to obtain the big picture by combining data step-by-step and finding the truth in large datasets. Freeing sensitivity from data noise should be an important step for sensitivity methodologists. In the second stage of the analysis, the average of the standard deviation values obtained for six different years, based on each method, was calculated and is presented in Table 6. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Years** & **MCRAT** & **SAW** & **TOPSIS** & **FUCA** \\ \hline
2010 & 0.0162 & 0.0039 & 0.0129 & 0.0048 \\
2012 & 0.0106 & 0.0074 & 0.0103 & 0.0018 \\
2014 & 0.0071 & 0.0019 & 0.0068 & 0.0016 \\
2016 & 0.0042 & 0.0011 & 0.0038 & 0.0010 \\
2018 & 0.0064 & 0.0016 & 0.0064 & 0.0016 \\
2023 & 0.0087 & 0.0023 & 0.0076 & 0.0023 \\ Mean & 0.0089 & 0.0030 & 0.0080 & **0.0022** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Mean standard deviations based on MCDM methods. Figure 4: Mean and standard deviation values between the fixed factors and methods. According to the results presented in Table 6 and Figure 5, which display the averages of standard deviation values across six different years, the methods can be ranked as follows: MCRAT > TOPSIS > SAW > FUCA.