## 5 Results
### Cost Estimation  
The cost estimation allows us to evaluate which configuration of the system is better for a given necessity in the explored scenario. Equation (23) represents the cost function used in this analysis, where \(w_{e}\) and \(w_{c}\) are the weights assigned to the energy consumption and the connectivity, respectively, and \(\bar{J}_{e}\) and \(\bar{J}_{c}\) are the normalized values for the figures of merit for the energy consumption and the connectivity obtained in [10]. This cost estimation does not include the communication range dynamics, as its figures do not show a correlation to the system's performance, as we have discussed in the previous section.  
\[J=w_{e}\bar{J}_{e}+w_{c}\bar{J}_{c} \tag{23}\]  
The normalized values of \(\bar{J}_{e}\) and \(\bar{J}_{c}\) are obtained using Equation (24), where \(x\) refers to the specific figure, either \(e\) for energy or \(c\) for connectivity, and \(y\) is the experiment for which the estimation is being calculated, while \(max(\bar{J}_{x})\) is the maximum value for the figure of merit for all of the experiments.  
\[\bar{J}_{x}=\frac{\bar{J}_{x,y}}{max(\bar{J}_{x})} \tag{24}\]  
Once we have the values for \(\bar{J}_{e}\) and \(\bar{J}_{c}\) for each experiment, we can just assume that the relation between the weights for the connectivity and the energy consumption follows Equation (25).  
\[w_{c}=1-w_{e} \tag{25}\]  
Then, we can assign a value from zero to one to the weight for the energy consumption to see how each experiment has behaved. The lowest value of the cost estimation indicates the best performance for the associated weights. Additionally, if we map all of the obtained results for the range assigned to both weights, we will obtain the result shown in Figure 13. This map represents how well a parameter set fits according to the assigned weights.  
The conclusion to the cost estimation is that when the energy consumption is the least relevant condition, up to 45.5% (or the connectivity is the most relevant condition from 54.5%), we should use a fixed transmission power set to the maximum. Additionally, when the energy is the most relevant condition, from 87.8% (or the connectivity is the least relevant condition up to 12.2%), we should still be using a fixed transmission power, but in this case set to a medium value. Additionally, the most important thing, when the energy consumption has a relevance between 45.5% and 87.8%, we should use the fuzzy control-based self-adaptive system with the configuration from Experiment e05. Of course, these results are valid for the experiments we have made. Additionally, they illustrate that there is a range of relevance for either the energy consumption and the connectivity where the use of a self-adaptive system provides better results than using fixed transmission power.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter Level** & \(ND_{R}\) & \(\xi_{ND}\) & \(k_{CR}\) \\ \hline \(SN_{p1}\) & 125.75 & 187 & 135.75 \\ \(SN_{p2}\) & 149.25 & 88 & 139.25 \\ \hline \(\Delta\bar{J}_{e}\) & **23.5** & **99** & **3.5** \\ \hline \hline \end{tabular}
\end{table}
Table 6: Figure of merit for communication range dynamics.