## 3 Results Obtained
### Application of the PROMETHEE II  
PROMETHEE II involves gathering data concerning the criteria of the vehicles. The values of the weights, maximizing and minimizing criteria, and the minimum and maximum criteria values must be known. The data used are the same as in Electre I. The table illustrates the nature of the criteria, including the weights and the maximum and minimum criteria values needed for normalization. The sum of the weights must equal zero. The maximizing criterion favors higher values, whereas the minimizing criterion prioritizes lower values [71]. Table 9 presents the input data processed by the PROMETHEE II method. Now, the data had to be normalized again to facilitate an effective comparison of the criteria on a scale from 0 to 1. As in ELECTRE I, it is necessary to distinguish between maximizing and minimizing criteria and select appropriate formulas. Formula (6) depicts the normalization for maximizing criteria, while Formula (7) illustrates the minimizing criterion normalization [72]. Maximizing criterion:  
\[p_{ij}=\frac{y_{ij}-\min(y_{i})}{\max(y_{i})-\min(y_{i})} \tag{6}\]  
Minimizing criterion:  
\[p_{ij}=\frac{\max(y_{i})-y_{ij}}{\max(y_{i})-\min(y_{i})} \tag{7}\]  
where \(P_{ij}\) refers to the normalized criterion value, \(max_{i}\) is the maximum value of the column, \(min_{i}\) suggests the minimum criterion value, and \(y_{ij}\) shows a normalized entry value. The values calculated using Formulas (6) and (7) are shown in Table 10. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Vehicle**} & **Maximum** & **Load-Carrying** & **Recharging** & **Purchase** & **Load-** & **Boaring** \\  & **Mileage [km]** & **Capacity [m\({}^{3}\)]** & **Speed [min]** & **Price** & **Capacity [t]** & **[kWh/100 km]** \\ \hline FORD & 284 & 15.1 & 34 & 81,040 & 1549 & 29.2 \\ RENAULT & 204 & 13 & 40 & 68,000 & 1308 & 34.5 \\ VW & 173 & 10.7 & 45 & 68,360 & 1700 & 21.5 \\ OPL & 330 & 6.6 & 35 & 62,640 & 1200 & 26.4 \\ PEUGEOT & 275 & 4.4 & 30 & 43,960 & 800 & 16.2 \\ \hline Weighting & 0.19 & 0.2 & 0.15 & 0.09 & 0.21 & 0.16 \\ Criterion nature & max & max & min & min & max & min \\ \hline min & 330 & 15.1 & 45 & 81,040 & 1700 & 34.5 \\ max & 173 & 4.4 & 30 & 43,960 & 800 & 16.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: PROMETHEE II—the input data. Source: authors. Calculation of preference indexes:  
\[\pi_{ij}^{h}=f\Big{(}y_{ih},y_{ih},q,p,v\Big{)} \tag{8}\]  
The next step involves transferring the preference data into positive preferences, where only values that indicate a preference of one vehicle over another are considered. The data transfer to positive preferences was calculated according to Formula (9) [73]. Positive preference data transfer:  
\[\pi_{ij}=\sum_{h=1}^{m}w_{h}\pi_{ij}^{h} \tag{9}\]  
where \(\pi_{ij}\) is the total preference index between \(i\) and \(j\), m refers to the number of criteria, \(w_{h}\) is the weight for criterion \(h\), and \(\pi_{ij}^{h}\) is the preference index for \(h\) between \(i\) and \(j\). In the event of a negative preference index, \(j\) is preferred over \(i\), and a value of 0 is input. Positive preferences are shown in Tables 16-20. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **A** & **B** & **C** & **D** & **E** & **F** \\ \hline v1v2 & 0.51 & 0.2 & 0.4 & 0 & 0.27 & 0.29 \\ v1v3 & 0.71 & 0.41 & 0.73 & 0 & 0 & 0 \\ v1v4 & 0 & 0.79 & 0.06 & 0 & 0.39 & 0 \\ v1v5 & 0.06 & 1 & 0 & 0 & 0.83 & 0 \\ \hline \end{tabular}
\end{table} 
Table 16: PROMETHE II—v1 preference transfer to positive preferences. Source: authors. \begin{table}
\begin{tabular}{c c c c c c} \hline  & **A** & **B** & **C** & **D** & **E** & **F** \\ \hline v2v1 & 0 & 0 & 0 & 0.35 & 0 & 0 \\ v2v3 & 0.2 & 0.21 & 0.33 & 0.01 & 0 & 0 \\ v2v4 & 0 & 0.59 & 0 & 0 & 0.12 & 0 \\ v2v5 & 0 & 0.8 & 0 & 0 & 0.56 & 0 \\ \hline \end{tabular}
\end{table} 
Table 17: PROMETHE II—v2 preference transfer to positive preferences. Source: authors.