## 4 Case Study
### Numerical Implementation
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline _Main Cannon_ & **T129** & **MI-** & **MI-** & **MI-** & **VIPER** & **Katran** & **Tiger** & **APACHE** & **Sikorsky** & **H215M** & **H160M** & _Punctuation_ & _Normalized_ _Punctuation_ \\ _System_ & **ATAK** & 0 & 0 & \(-1\) & \(-1\) & \(-2\) & 0 & 1 & 1 & \(-2\) & 0.333 \\ VIPER & 0 & 0 & \(0\) & \(-1\) & \(-1\) & \(-2\) & 0 & 1 & 1 & \(-2\) & 0.333 \\ Katran & 1 & 1 & 1 & 0 & \(0\) & \(-1\) & 1 & 2 & 2 & 7 & 0.667 \\ Tiger HAD & 1 & 1 & 1 & 0 & 0 & \(-1\) & 1 & 2 & 2 & 7 & 0.667 \\ APACHE & 2 & 2 & 2 & 1 & 1 & 0 & 2 & 3 & 3 & 16 & 1 \\ Sikorsky S-70 & 0 & 0 & \(0\) & \(-1\) & \(-1\) & \(-2\) & 0 & 1 & 1 & \(-2\) & 0.333 \\ H215M & \(-1\) & \(-1\) & \(-1\) & \(-2\) & \(-2\) & \(-1\) & 0 & 1 & 1 & \(-2\) & 0.333 \\ VH2R & 0 & 0 & 0 & \(-1\) & \(-1\) & \(-2\) & 0 & 1 & 1 & \(-2\) & 0.333 \\ Katran & 1 & 1 & 1 & 0 & 0 & \(-1\) & 1 & 2 & 2 & 7 & 0.667 \\ Tiger HAD & 1 & 1 & 1 & 0 & 0 & \(-1\) & 1 & 2 & 2 & 7 & 0.667 \\ APACHE & 2 & 2 & 2 & 1 & 1 & 0 & 2 & 3 & 3 & 16 & 1 \\ Sikorsky S-70 & 0 & 0 & 0 & \(-1\) & \(-1\) & \(-2\) & 0 & 1 & 1 & \(-2\) & 0.333 \\ H215M & \(-1\) & \(-1\) & \(-1\) & \(-2\) & \(-2\) & \(-3\) & \(-1\) & 0 & 0 & \(-11\) & 0 \\ H160M & \(-1\) & \(-1\) & \(-1\) & \(-2\) & \(-2\) & \(-3\) & \(-1\) & 0 & 0 & \(-11\) & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Evaluation of alternatives under qualitative criterion _Main cannon system_. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline _Missiles_ & **T129** & **MI-** & **MI-** & **VIPER** & **Katran** & **Tiger** & **APACHE** & **Sikorsky** & **H215M** & **H160M** & _Punctuation_ & _Normalized_ _Punctuation_ \\ _System_ & **ATAK** & 35M & & & & & & & & & \\ \hline T129 ATAK & 0 & \(-1\) & \(-1\) & \(-1\) & 0 & \(-1\) & 0 & 1 & 1 & \(-2\) & 0.5 \\ MI-35M & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 2 & 2 & 7 & 1 \\ VIPER & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 2 & 2 & 7 & 1 \\ Katran & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 2 & 2 & 7 & 1 \\ Tiger HAD & 0 & \(-1\) & \(-1\) & \(-1\) & 0 & \(-1\) & 0 & 1 & 1 & \(-2\) & 0.5 \\ APACHE & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 2 & 2 & 7 & 1 \\ Sikorsky S-70 & 0 & \(-1\) & \(-1\) & \(-1\) & 0 & \(-1\) & 0 & 1 & 1 & \(-2\) & 0.5 \\ H215M & \(-1\) & \(-2\) & \(-2\) & \(-2\) & \(-1\) & \(-2\) & \(-1\) & 0 & 0 & \(-11\) & 0 \\ H160M & \(-1\) & \(-2\) & \(-2\) & \(-2\) & \(-1\) & \(-2\) & \(-1\) & 0 & 0 & \(-11\) & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Evaluation of alternatives under qualitative criterion _Missiles system_. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline _Armament_ & **T129** & **MI-** & **MI-** & **VIPER** & **Katran** & **Tiger** & **APACHE** & **Sikorsky** & **H215M** & **H160M** & _Punctuation_ & _Normalized_ _Punctuation_ \\ _Subsystems_ & **ATAK** & **35M** & & & & & & & & & \\ \hline T129 ATAK & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 2 & 0 & 4 & 0.905 \\ MI-35M & \(-1\) & 0 & \(-1\) & \(-1\) & \(-1\) & \(-1\) & 0 & 1 & \(-1\) & \(-5\) & 0.476 \\ VIPER & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 3 & 0 & 6 & 1 \\ Katran & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 2 & 0 & 4 & 0.905 \\ Tiger HAD & 0 & 1 & -1 & 0 & 0 & 0 & 1 & 2 & 0 & 3 & 0.857 \\ APACHE & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 2 & 0 & 4 & 0.905 \\ Sikorsky S-70 & \(-1\) & 0 & \(-1\) & \(-1\) & \(-1\) & \(-1\) & 0 & 1 & \(-1\) & \(-5\) & 0.476 \\ H215M & \(-2\) & \(-1\) & \(-3\) & \(-2\) & \(-2\) & \(-2\) & \(-1\) & 0 & \(-2\) & \(-15\) & 0 \\ H160M & \(0\) & 1 & 0 & 0 & 0 & 0 & 1 & 2 & 0 & 4 & 0.905 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Evaluation of alternatives under qualitative criterion _Technological level_. It is noteworthy that the V-shape and V-shape I functions are used to enable a preference limit, that is, any alternative above this limit presents a strict preference as to another within the specific criterion, and also for providing to identify a linear performance at least that it is, for example, when analyzing the speed of the helicopters.