# A New Centralized Clustering Algorithm for Wireless Sensor Networks
## 5 Conclusions  
In the present paper, we propose a new centralized clustering algorithm based on a Type-2 Fuzzy system. This method schedules the CH selection in a round manner, so that the control message exchange is reduced (executed every'skip' rounds) but the data transmission is not compromised. The most appropriate value for the skip parameter was judiciously determined according to the reliability and durability of the network. It was demonstrated that the proposed algorithm outperforms the other tested algorithms (including centralized and distributed methods). The results depicted in Figures 10-12 also show that algorithms based on Type-2 Fuzzy system are more capable of adapting to different network layouts when compared with the algorithms that use Type-1 fuzzy systems. Moreover, the centralized clustering algorithms obtained better results than the distributed ones due to the common knowledge that the base station has about the whole network. However, as can be observed in Figures 7-9 when achieving higher values of HND and LND with CSBA, FND will suffer a serious decrease. This will impact on the reliability of the network. The value chosen for the skip parameter may not suit other network layouts with a different amount of nodes or field dimensions (even when the selected skip value was valid for the three tested scenarios). In addition, CSBA does not take into account nodes which die during skip intervals. If those nodes are CHs, the reliability of the system could be seriously compromised and some information collected by those CHs could be lost.  
Therefore, as future work, we will address the dynamic determination of the skip value with an additional intelligence-based system in order to achieve a better adaptability for different network layout, number of nodes and network dynamics. That new intelligent system, hosted in the BS, would monitor the evolution of the network (e.g., number of node deaths, average energy in network areas or concentration of alive nodes), to adapt the skip value in order to increase the network lifetime. Moreover, the BS could take into account events, such as the death of a CH during the skip interval or new thresholds and variables to elect CHs dynamically (even during a skip). From the behaviour observed in the input variables of the T2 FIS, a new design of those fuzzy variables would be necessary in order to tune the design of the fuzzy sets and their fuzzification.  
Figure 12: FND, HND and LND for 150 nodes in a 100 m \(\times\) 100 m area with BS at (50, 50) m.  
**Author Contributions:** Conceptualization, A.-J.-Y.-D., J.-C.C.-M., A.T.-C. and A.-J.-L.-S.; methodology, [PERSON]-J.-Y.-D., J.-C.-M. and [PERSON]-J.-L.-S.; software, [PERSON]-J.-Y.-D., [PERSON]-C.-M. and [PERSON]-J.-L.-S.; validation, A.-J.-Y.-D., J.-C.-M., A.T.-C. and [PERSON]-J.-S.-C.; formal analysis, [PERSON]-J.-Y.-D. and [PERSON]-J.-S.-C.; investigation, [PERSON]-J.-Y.-D., J.-C.-M., and A.T.-C.; resources, A.-J.-Y.-D. and J.-C.C.-M.; writing-original draft preparation, [PERSON]-J.-Y.-D., [PERSON]-J.-L.-S. and J.-C.C.-M.; writing-review and editing, [PERSON], and [PERSON].  
**Funding:** This research was partially funded by Plan Propio de Investigacion de la Universidad de Malaga (Spain).  
**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.