## 4 Application
### Ranking Alternatives Using the MCDM Methods  
In the second stage of the proposed model, the MCRAT, SAW, TOPSIS, and FUCA methods were employed to evaluate the alternatives. In this section, since each criterion range in the decision matrix is the same or the value range is narrow (scores between 1 and 5), the analyses were performed without normalization. In this context, the MCDM results obtained using various normalization techniques were first compared with the non-normalized MCDM results, revealing a strong correlation between the two. In this section, to avoid any complexity due to the large number of outputs, only the MCRAT results will be presented. \begin{table}
\begin{tabular}{c c} \hline \hline
**Indicators** & **Descriptions** \\ \hline Customs (C1) & The effectiveness of customs and border management processes. \\ Infrastructure (C2) & The standard of infrastructure related to trade and transportation \\ International Shipments (C3) & The convenience of organizing cost-effective \\ Logistics Competence and Quality (C4) & The skill and excellence of logistics services \\ Timeliness (C5) & The capability to monitor and trace shipments \\ Tracking and Tracing (C6) & The rate at which shipments arrive at their \\ destinations within the promised or & \\ anticipated delivery timeframe \\ \hline \hline \end{tabular} Source: [11].  
\end{table} 
Table 1: Explanations of the LPI indicators. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \(\mathbf{C_{1}}\) & \(\mathbf{C_{2}}\) & \(\mathbf{C_{3}}\) & \(\mathbf{C_{4}}\) & \(\mathbf{C_{5}}\) & \(\mathbf{C_{6}}\) \\ \hline
2010 & & 0.1993 & 0.2650 & 0.0914 & 0.1783 & 0.1712 & 0.0948 \\
2012 & & 0.1815 & 0.2376 & 0.1289 & 0.1747 & 0.1705 & 0.1067 \\
2014 & w\({}_{\text{j}}\) & 0.1942 & 0.2309 & 0.1167 & 0.1659 & 0.1595 & 0.1329 \\
2016 & & 0.1813 & 0.2242 & 0.1315 & 0.1712 & 0.1814 & 0.1105 \\
2018 & & 0.1807 & 0.2258 & 0.1268 & 0.1804 & 0.1743 & 0.1121 \\
2023 & & 0.1776 & 0.2271 & 0.1176 & 0.1687 & 0.1214 & 0.1876 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Criteria weights. Figure 2: Importance of criteria weights between 2010 and 2023. As shown in Table 3, there is a very high correlation between the MCRAT results obtained using different normalization techniques and those without normalization. Moreover, a full correlation was observed between the results generated using the max normalization technique and the non-normalized MCRAT results. A similar situation applies to the other MCDM methods used in this study as well. These findings suggest that, for this study, normalization is not necessary when applying the MCDM methods. In this context, the MCRAT method steps (Equations (7)-(16)) were applied sequentially. In 2010, Germany, the Netherlands, and Singapore were the leading countries in logistics performance, while Cuba, Rwanda, and Guinea-Bissau were at the bottom of the rankings. In 2012, Singapore, Hong Kong SAR, China, and Germany achieved the highest LPI scores, whereas Haiti, the Republic of Congo, and Dijbouti recorded the lowest scores. For 2014, Germany, the Netherlands, and Singapore continued to lead, while Afghanistan, the Republic of Congo, and the Democratic Republic of Congo were at the bottom. In 2016, Germany, Sweden, and the Netherlands occupied the top positions, with Lao PDR, Haiti, and the Syrian Arab Republic at the lowest ranks. By 2018, Germany, Japan, and Sweden emerged as the top performers among 118 countries, while Haiti, Angola, and Afghanistan were ranked the lowest. In 2023, Singapore, Switzerland, and Finland exhibited the highest logistics performance, while Cameroon, Afghanistan, and Libya were at the bottom of the rankings. In the 2010 World Bank LPI report, Germany emerges as the top-performing country with an LPI score of 4.13. Singapore and Sweden follow Germany with LPI scores of 4.10 and 4.09, respectively. Rwanda, Cuba, and Guinea-Bissau occupy the bottom three ranks with LPI scores of 2.04, 2.68, and 2.10, respectively.