## 3 Results Obtained
### Application of the ELECTRE I
Minimum criterion:  
\[y^{\prime}_{ih}=\frac{y_{ih}-\min\limits_{i}(y_{ih})}{\max\limits_{i}(y_{ih})- \min\limits_{i}(y_{ih})} \tag{2}\]  
Maximum criterion:  
\[y^{\prime}_{ih}=\frac{\max\limits_{i}(y_{ih})-y_{ih}}{\max\limits_{i}(y_{ih})- \min\limits_{i}(y_{ih})} \tag{3}\]  
where \(y^{\prime}_{ih}\) is a normalized value, \(max_{i}\) is the maximum criterion value, \(min_{i}\) is the minimum criterion value, and \(y_{ih}\) is the normalized entry value [77]. Table 5 suggests the normalization process. The following step involves the creation of a concordance table to illustrate the degree to which one variable dominates another (see Table 6), using Formula (4) [68]. Concordance calculation:  
\[c_{ij}=\sum\
olimits_{h\in H_{ij}}w_{h} \tag{4}\]  
where \(H\!ij\) is a criteria set where \(i\) variable dominates \(j\) variable. The discordance table (see Table 7) depicts whether a significantly worse variable exists, using Formula (5) [68]. \begin{table}
\begin{tabular}{c c c c c c} \hline
**C** & **FORD** & **RENAULT** & **VW** & **OPEL** & **PEUGEOT** \\ \hline FORD & - & 0.9 & 0.54 & 0.56 & 0.6 \\ RENAULT & 0.1 & - & 0.79 & 0.41 & 0.6 \\ VW & 0.46 & 0.21 & - & 0.57 & 0.41 \\ OPEL & 0.44 & 0.59 & 0.43 & - & 0.4 \\ PEUGEOT & 0.4 & 0.4 & 0.59 & 0.6 & - \\ \hline \end{tabular}
\end{table} 
Table 6: Electre I—concordance table. Source: authors. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Vehicle** & **Maximum** & **Load-Carrying** & **Recharging** & **Purchase** & **Load-** & **Consumption** \\
**Mileage [km]** & **Capacity [m\({}^{3}\)]** & **Speed [min]** & **Price** & **Bearing** & **Capacity [t]** & **[kWh/100 km]** \\ \hline FORD & 0.71 & 1 & 0.73 & 0 & 0.83 & 0.29 \\ RENAULT & 0.2 & 0.8 & 0.33 & 0.35 & 0.56 & 0 \\ VW & 0 & 0.59 & 0 & 0.34 & 1 & 0.71 \\ OPEL & 1 & 0.21 & 0.67 & 0.5 & 0.44 & 0.44 \\ PEUGEOT & 0.65 & 0 & 1 & 1 & 0 & 1 \\ \hline Weighting & 0.19 & 0.2 & 0.15 & 0.09 & 0.21 & 0.16 \\ Criterion nature & max & max & min & min & max & min \\ \hline \end{tabular}
\end{table} 
Table 5: Electre I—normalization. Source: authors. Discordance calculation:  
\[d_{ij}=\max_{h\in H_{ij}^{n}}\left(\frac{y_{jh}-y_{ih}}{\max_{i}(y_{ih})-\min_{i}( y_{ih})}\right) \tag{5}\]  
where \(c_{ij}\geq c^{\star}\) and \(d_{ij}\), then \(p_{ij}=1\), otherwise \(p_{ij}=0\) (see Tables 7 and 8). The evaluation involves threshold values calculated by the arithmetic mean from the concordance and discordance table [69]. * C \(\geq\) 0.5--concordance threshold;
* D \(\leq\) 0.70--discordance threshold. Matrix \(p\) requires that the concordance and discordance thresholds are not exceeded. The possible entry value is either 1, indicating that both threshold values are satisfied (preferred variable), or 0, indicating that one or both threshold values are not satisfied (non-preferred variable or it is impossible to prefer the variables based on the threshold values) [70]. Matrix \(p\) (see Table 8), in terms of the ELECTRE I method, represents the final evaluation of preferences among individual variants after the application of concordance and discordance procedures. * \(i\) variable is preferred over \(j\) variable, if \(p_{ij}=1\);
* the evaluation of the \(p\) matrix reveals dominant variables regarding the criteria. Crucial findings:
* FORD is the strongest (the compromise) variant because it dominates over RENAULT, VW, as well as OPEL,
* OPEL only dominates over RENAULT but does not outweigh other variants,
* PEUGEOT dominates only over OPEL,
* RENAULT and VW are the weakest variants because they have no preference (all the values in their rows are 0). Outcomes from the decision-making process in terms of the van selection based on the identified criteria are as follows:  
* FORD represents an explicit compromise variant because it dominates over the other three considered variants (vans),