## 4 Case Study
### Numerical Implementation  
The analyzed problem handles the priory to rank and identifies a favorable alternative regarding the employment of attack helicopters in BN naval operations. Considering the set of variables, nine alternatives were evaluated under fourteen criteria, being six qualitative and eight quantitative. Table 4 details the evaluation matrix, exposing the performance of the alternatives in each criterion. The qualitative performance, expressed by verbal terms, is clarified in the following procedures. The proposed approach starts evaluating the alternatives regarding the qualitative criteria: _Technological level, Main cannon system, Missiles system, Armament subsystems, Armor level,_ and _Employment flexibility_. The consulted officers exposed their opinions, providing the preference punctuation between alternatives. In each qualitative criterion, is presented the preference relation between each pair of alternatives, providing the cardinal punctuations of alternatives in the analysis, as exposed in the following Tables 5-10. Regarding the evaluation of alternatives setting the preferences by ordinal scale, it was possible to obtain cardinal punctuation to each alternative in a qualitative criterion. As exposed in Section 3.2.1, the alternative punctuations are submitted in a maximization process in search to obtain the difference between each pair and convert it in a final preference index of each pair of alternatives in each criterion, represented by a matrix. Following the modeling procedure, the alternatives are evaluated under the quantitative criteria, sustaining the process of the PROMETHEE method. It was defined, for each quantitative criterion, if it is a criterion of benefit (maximization) or cost (minimization), and which type of preference function (Figure 2) is suitable to provide the final preference degree. Table 11 presents all information regarding the necessary data for quantitative evaluation, highlighting the use of the preference functions _V-shape_ and _V-shape I_. The selected preference functions enabled to perform the alternatives concerning the limits of indifference (\(q\)) and preference (\(p\)), providing relations of non-preference, linear preference, and strict preference. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & **T129** & **MI-35M** & **VIPER** & **Katran** & **Tiger** & **APACHE** & **Sikosky** & **H215M** & **H160M** \\ \hline _Technological level_ & Advanced & Proficient & Advanced & Advanced & Advanced & & & & & \\ _Main camon system_ & Proficient & Proficient & Proficient & Advanced & Advanced & & & & & \\ _Missiles system_ & Proficient & Advanced & Advanced & & & & & & \\ _Armament subsystems_ & Advanced & Proficient & Advanced & Advanced & & & & & \\ _Armor level_ & High Advanced & Advanced & Advanced & & & & & & \\ _Employment flexibility_ & Good & Good & Good & Good & Average & Good & Average & Average & & \\ _Maximum speed_ & 281 & 310 & 370 & 300 & 271 & 279 & 315 & 278 & 325 \\ (Km/h) & 269 & 240 & 257 & 260 & 230 & 269 & 223 & 258 & 255 \\ _Range_ (Km) & 537 & 460 & 485 & 460 & 740 & 476 & 450 & 780 & 848 \\ _Autonomy_ (h) & 3 & 3.5 & 3.5 & 3.5 & 2.7 & 3 & 3 & 3.9 & 4.5 \\ _Service calling_ (m) & 6096 & 5400 & 6000 & 5500 & 4000 & 6096 & 5837 & 3450 & 5900 \\ _Maximum payload_ (Kg) & 2710 & 2400 & 2615 & 3300 & 2030 & 2835 & 4045 & 3000 & 1500 \\ _Troop capacity_ (Qt) & 0 & 8 & 0 & 0 & 0 & 0 & 13 & 20 & 12 \\ _Length_ (m) & 13.64 & 21.6 & 17.8 & 16 & 13.85 & 14.68 & 15.26 & 15.5 & 14 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Evaluation matrix regarding the helicopters under qualitative and quantitative criteria.