## 4 Illustrative Example
### Group Decision-Making Process  
1. Preference among alternatives. Once the preferences of each expert for each alternative have been calculated, we aggregate them to obtain the overall level of preference for each of the alternatives. The closer the value is to 1, the more popular that alternative is among the experts. We can see the result of this calculation on Table 7.
2. Calculation of the degree of subjectivity. The degree of subjectivity in the opinions given in the debate, both positive and negative, can be calculated using Expressions (8) and (9). Subjectivity allows us to extract more information about how the experts are performing in the debate and allows us to go beyond the simple opinion they provide. If we compare, for example, the preference values provided by \(e_{1}\) to the ones provided by \(e_{2}\), it is possible to see, in Table 7, that, in both cases, the obtained value is 0.94. However, when applying the calculation of the subjectivity, which is proposed as a novelty in this paper, of each of them, in relation to positivity, it can be seen that \(e_{2}\) obtained a higher value (9.31%) despite making fewer contributions. Consequently, the implication of \(e_{2}\) in the debate is higher than \(e_{1}\). Moreover, it is possible to conclude that the degree of positivity of \(e_{2}\) is higher than the one of \(e_{1}\). In terms of negativity, the value obtained is similar. In Table 8, it is possible to see the subjectivity values for the alternative #WaterEc. 3. Consensus. To obtain the consensus associated with the group decision-making process we are carrying out, we can apply Expression (7). The value obtained measures the consensus reached by all experts during the discussion. Table 9 shows the consensus reached by each pair of experts. In Table 10 the calculation of the consensus reached for each alternative can be seen. The higher the value obtained, the greater the agreement reached among all experts on the alternative. The calculation of the overall consensus can be seen below: \[\widetilde{CS}=\frac{\sum CS}{n}\] \[\widetilde{CS}=\frac{3.6}{4}=0.9\] As the overall consensus reaches a value of 0.9, the threshold of \(\gamma=0.75\) set at the beginning of the decision-making process is exceeded. Therefore, it can be determined that there is consensus among the experts and, consequently, the final ranking of alternatives can be calculated. 4. Collective preference matrix and final ranking calculation. To obtain the ranking we first obtain the collective preference matrix. Once obtained, we will use Expression (7) to calculate the final ranking of alternatives. We can see the results of these calculations in Table 11. Therefore, the alternatives are ranked as shown: \[R=\{\#EnergyEC,\#WaterEc,\#TracksEC,\#InternetEC\}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**E** & **\#WaterEc** & **\#EnergyEc** & **\#InternetEc** & **\#TracksEc** & **Mean** \\ \hline \(e_{1}\) & 0.94 & 0.83 & 0.85 & 0.77 & 0.85 \\ \hline \(e_{2}\) & 0.94 & 0.83 & 0.43 & 0.67 & 0.72 \\ \hline \(e_{3}\) & 0.92 & 0.80 & 0.40 & 0.80 & 0.73 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Mean preference for each of the alternatives. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Exerts** & **\#A** & **\#E** & **\#I** & **\#V** \\ \hline \(e_{1}-e_{2}\) & 1.00 & 1.00 & 0.58 & 0.90 \\ \hline \(e_{1}-e_{3}\) & 0.99 & 0.97 & 0.55 & 0.97 \\ \hline \(e_{1}-e_{4}\) & 0.97 & 1.00 & 0.89 & 0.97 \\ \hline \(e_{1}-e_{5}\) & 0.90 & 0.95 & 0.83 & 0.91 \\ \hline \(e_{2}-e_{3}\) & 0.99 & 0.97 & 0.97 & 0.87 \\ \hline \(e_{2}-e_{4}\) & 0.97 & 1.00 & 0.69 & 0.87 \\ \hline \(e_{2}-e_{5}\) & 0.90 & 0.95 & 0.75 & 0.81 \\ \hline \(e_{3}-e_{4}\) & 0.99 & 0.97 & 0.66 & 1.00 \\ \hline \(e_{3}-e_{5}\) & 0.91 & 0.92 & 0.72 & 0.94 \\ \hline \(e_{4}-e_{5}\) & 0.92 & 0.95 & 0.94 & 0.94 \\ \hline \(\mathbf{Consensus}\) & \(\mathbf{0.95}\) & \(\mathbf{0.97}\) & \(\mathbf{0.76}\) & \(\mathbf{0.92}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Final ranking of alternatives.