## 5 An Innovative Robustness and Reliability Analysis  
To validate the proposed integrated model, the impact of altering the criterion weights on the ranking results was examined. In this context, by adjusting the weight of each criterion, 105 scenarios were created to assess their effects on the preference levels of the alternatives. In previous studies, some researchers have modified the weight of the most important criterion [58], interchanged criterion weights [59, 60], or made certain criteria more significant [60]. This study, however, considers the impact of all criteria on the results. The criterion weights presented in Table 4 were analyzed separately for six different sets and across four different MCDM methods to perform a comparative analysis, resulting in a total of over 2500 outcomes. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \(\mathbf{C_{1}}\) & \(\mathbf{C_{2}}\) & \(\mathbf{C_{3}}\) & \(\mathbf{C_{4}}\) & \(\mathbf{C_{5}}\) & \(\mathbf{C_{6}}\) \\ \hline s1 & 0.34 & 0.21 & 0.21 & 0.08 & 0.08 & 0.08 \\ s2 & 0.34 & 0.21 & 0.08 & 0.21 & 0.08 & 0.08 \\ s3 & 0.34 & 0.21 & 0.08 & 0.08 & 0.21 & 0.08 \\ s4 & 0.34 & 0.21 & 0.08 & 0.08 & 0.08 & 0.21 \\ s5 & 0.37 & 0.23 & 0.1 & 0.1 & 0.1 & 0.1 \\ s103 & 0.12 & 0.12 & 0.12 & 0.26 & 0.26 & 0.12 \\ s104 & 0.12 & 0.12 & 0.12 & 0.26 & 0.12 & 0.26 \\ s105 & 0.12 & 0.12 & 0.12 & 0.12 & 0.26 & 0.26 \\ \hline \end{tabular}
\end{table} 
Table 4: Criterion weights for different scenarios. Figure 3: The six-year average of the rankings from the four MCDM methods and the LPI for different countries. In this section, the degree, direction, and nature of sensitivity are examined using the innovative sensitivity analysis approach proposed by [13]. According to this approach, low sensitivity (as indicated by standard deviation) in MCDM rankings corresponds to a high correlation (rho) with a fixed external factor. However, it is important to acknowledge that sensitivity is influenced by various components, including the selected MCDM method, the characteristics of the problem, the type of data, and the weighting coefficients within the MCDM framework [31] However, while an external ranking was used in these studies, we determined an internal fixed factor. Thus, it eliminates the difficulty for decision-makers to search for an external factor in sensitivity analysis. We preferred Entropy-based MCDM as an external factor. We focused on the motion and sensitivity of the entire sequence because we considered that some approaches that consist of simply observing the best alternative in the literature may be shallow and inaccurate. Moreover, we preferred to focus on the motion and sensitivity of the entire sequence, as we thought that some approaches in the literature that consist solely of observing the best alternative may be superficial and inaccurate. Accordingly, the impact of different weighting techniques on the results of the MCRAT method was assessed, using the Entropy-MCRAT results as the fixed external factor. In the first stage of the analysis, the MCRAT results obtained from 105 scenarios were compared with the Entropy-MCRAT results. For the SAW, TOPSIS, and FUCA results, the Entropy-SAW, Entropy-TOPSIS, and Entropy-FUCA rankings were considered as fixed factors. Additionally, the average correlations between the external fixed factor and the methods are presented in Table 5.  
Table 5 above is the first sign of interesting findings. The change in sensitivity results depending on the dataset shows that researchers who will conduct sensitivity analysis need to use very large datasets if they want to see the ultimate winner. When evaluating the results presented in Table 5 and Figure 4 on an annual basis, the methods with the highest and lowest average scores for 2010 are SAW and MCRAT, respectively. According to the standard deviation values, the ranking of methods is as follows: MCRAT\(>\) TOPSIS\(>\) FUCA\(>\) SAW.