## 6 Discussion and Future Works
### Future Works
#### 6.1.1 Detailed Description of the Proposal for Further Exploration of the Use of Weighted Links  
The proposed fuzzy control-based self-adaptive system has been defined to use the node degree as a reference to make an estimated adjustment of the transmission power in order to achieve a minimum connectivity represented by the expression k-connected. The results analyzed in this paper and already discussed show that the node degree is a value that changes even when there is no change in the network parameters. This happens because some nodes can and usually will be located in a frontier area with respect to a reference node. Thus, a minor change in the environment conditions can cause their connectivity to the reference node to be interment.  
Just take a look at Figure 16a. In this figure, we have depicted a potential scenario. The reference node is labeled as \"1\", and a disc communication range approach is used for explaining the theory. There are two discs in the figure. The inner disc represents the area where the connectivity is not affected by the environment. Of course, the quality of the communication can and will vary, but the nodes inside this disc will always appear as neighbors to Node \"1\". The outer disc represents the limit of the communication range for Node \"1\", and the ring between the inner and the outer discs is the area of the nodes that can be neighbors or not at different times.  
If we just use the same probabilistic approach as defined for the system under test, Node \"1\" can have any number from two to six neighbors at any time. If the \(ND_{R}\) and the \(\xi_{ND}\) values are selected, two neighbors are not enough to guarantee the network connectivity; we can assure that there will be iterations of the control loop where the transmission power will be readjusted. Additionally, in a case like the one proposed, a readjustment of the transmission power may not be necessary, or even worse, can introduce new variations on the environment breaking the steady state of the networks.  
Therefore, it could be interesting to explore the use of other probabilistic approaches, like considering the quality of the communication of every potential neighbor besides the node degree. For instance, in Figure 16, we have assigned a value between 0.0 and 1.0 to each potential neighbor. In this example, the value represents the probability that the node will be seen as a neighbor from Node \"1\". We can then sum the weights, so we can say that the connectivity quality of the neighborhood for Node \"1\" is 3.4.  
**Acknowledgments:** This work has been supported by the European project \"Design, Monitoring, and Operation of Adaptive Networked Embedded Systems\" (DEMANES) (Project Code ARTEMIS-JU: 295372) and \"Ministerio de Industria, Energia y Turismo\" of Spain (Project Code ART-010000-2012-2).  
**Author Contributions:** [PERSON] focused on designing the self-adaptive control system, considering feedback control loop theory, and on defining the corresponding fuzzy-logic functions. [PERSON], [PERSON] and [PERSON] have analyzed and studied the suitability and feasibility of the tested approach consisting of adapting WSAN nodes' transmission power to assure each node has a minimum number of neighbors, as described previously. [PERSON], [PERSON] and [PERSON] carried out and deployed in the SunSPOT nodes comprising the WSAN under study the software modules and components described in previous sections. They also ran the experiments and made the assessments, taking into account the outcomes from the tests.  
**Conflicts of Interest:** The authors declare no conflict of interest.