## 4 Case Study
### Result Analysis  
As explored in the previous sections, the proposed model enables three models of results in search to obtain a sensitivity analysis of the problem. The three models are based on a partial, complete, and intervals outranking. In the software, a graphical representation was enabled, generating three charts after entering data. Figure 5 exposes the graphical analysis interface. Remembering that the positive and negative flow provide the partial ranking, the complete ranking handles the net flows, and the ranking by intervals is built by the lower and upper limit, with all values detailed in Table 14.  
First, the performances concerning the partial outranking were analyzed. In the Partial Pre-ordering graphic exposed in Figure 5, the right line represents the positive flows and the left line the negative flows, whereas the higher the positive and the lower the negative, the better is the alternative, represented by the crossing of lines. It is possible to note that the alternative with the best performance is the helicopter APACHE, presenting the highest positive flow and the lowest negative flow, exposing a total preference over the set. The following most preferable alternatives are Katran, VIPER, and T129 ATAK, respectively. Concerning the alternatives, Tiger and Sikorsky S-70, both presented an incompatible relation regarding the alternative MI-35M. In this analysis, the alternative H160M becomes preferable only over H215M, which was worse than all alternatives. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & \begin{tabular}{c} **T129** \\ **ATAK** \\ \end{tabular}  & **MI-35M** & **VIPER** & **Katran** & \ \begin{tabular}{c} **Tiger** \\ **HAD** \\ \end{tabular}  & **APACHE** & \begin{tabular}{c} **Sikorsky** \\ **S-70** \\ \end{tabular}  & **H215M** & **H160M** & \(\boldsymbol{\phi^{*}}\) & \(\boldsymbol{\phi}\) \\ \hline T129 & 0 & 0.020 & 0.008 & 0.007 & 0.015 &  
The second analysis is based on the Total Pre-ordering as exposed in Figure 5, just ranking the alternatives over the line of net flows. In this evaluation, the alternative APACHE continued to present the best ranking, preceded by Katran, VIPER, T129 ATAK, Tiger, MI-35M, Sikorsky S-70, H160M, and H215M, respectively, in this order. Even presenting a simple format of analysis, the model enables to identify preference relation in cases that exposed an incompatible relation in the previous analysis, where it was possible to note regarding the alternatives Tiger and Sikorsky S-70 concerning the alternative MI-35M. As presented in Table 14 and Figure 5, the intervals of alternatives based on the standard error of 0.032 were constructed. Based on the graph, a preference relation is indicated, when there is no intersection between intervals, otherwise, a relationship of indifference is indicated. This analysis model makes it possible to understand if an alternative is relatively superior concerning another or if the difference between the preferences is so small that both can become equivalent. It is noticeable that in this type of evaluation, the alternative APACHE becomes indifferent regarding alternatives Katran and, by a minimum difference, also becomes indifferent to VIPER. It is possible to observe that the alternatives Tiger, \begin{table}
\begin{tabular}{c c c c} \hline \hline  & _Net Flow (\(\phi\))_ & _Lower Limit (\(x\))_ & _Upper Limit (\(y\))_ \\ \hline T129 ATAK & 0.051 & 0.019 & 0.083 \\ MI-35M & \(-\)0.044 & \(-\)0.076 & \(-\)0.012 \\ VIPER & 0.074 & 0.042 & 0.106 \\ Katran & 0.101 & 0.069 & 0.133 \\ Tiger HAD & \(-\)0.018 & \(-\)0.05 & 0.014 \\ APACHE & 0.136 & 0.104 & 0.168 \\ Sikorsky S-70 & \(-\)0.052 & \(-\)0.084 & \(-\)0.020 \\ H215M & \(-\)0.148 & \(-\)0.180 & \(-\)0.116 \\ H160M & \(-\)0.100 & \(-\)0.132 & \(-\)0.068 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Lower and upper limits for construction of preference analysis by intervals. Figure 5: Charts generated by the web platform based in the three models of preference analysis.