###### Abstract  
Clustering algorithms are necessary in Wireless Sensor Networks to reduce the energy consumption of the overall nodes. The decision of which nodes are the cluster heads (CHs) greatly affects the network performance. The centralized clustering algorithms rely on a sink or Base Station (BS) to select the CHs. To do so, the BS requires extensive data from the nodes, which sometimes need complex hardware inside each node or a significant number of control messages. Alternatively, the nodes in distributed clustering algorithms decide about which the CHs are by exchanging information among themselves. Both centralized and distributed clustering algorithms usually alternate the nodes playing the role of the CHs to dynamically balance the energy consumption among all the nodes in the network. This paper presents a distributed approach to form the clusters dynamically, but it is occasionally supported by the Base Station. In particular, the Base Station sends three messages during the network lifetime to reconfigure the _skip_ value of the network. The _skip_, which stands out as the number of rounds in which the same CHs are kept, is adapted to the network status in this way. At the beginning of each group of rounds, the nodes decide about their convenience to become a CH according to a fuzzy-logic system. As a novelty, the fuzzy controller is as a Tagaki-Sugeno-Kang model and not a Mandami-one as other previous proposals. The clustering algorithm has been tested in a wide set of scenarios, and it has been compared with other representative centralized and distributed fuzzy-logic based algorithms. The simulation results demonstrate that the proposed clustering method is able to extend the network operability. wireless sensor networks; clustering; interval Type-2 fuzzy system 20202020  
This last device is called the sink, gateway, or Base Station (BS). The BS is usually connected to the power grid and it usually has greater computing power, so it does not have the scarce resources of the sensors. Precisely, the power resources in the sensors constitute a limiting characteristic of the WSN as it can prevent the network from operating correctly, that is, gathering all the required information and transmitting it to the BS. Therefore, one of the main challenges of the WSN is to increase the lifetime of the network to avoid nodes depleting their batteries when accomplishing unnecessary tasks. In this sense, one of the most useful techniques is clustering, whereas traditional routing appears better suited for larger networks. A typical example of clustering is found in Figure 1. Among all the nodes, some of them are chosen to become Cluster Heads (CH). The CHs act as gatherers of data of the associated nodes, also referred to as contributing nodes. The nodes transmit their measurements to only one CH, which usually is the one that is closest to them. Then, each CH aggregates the information from its group and relays it to the BS. This technique avoids that all the nodes would have to communicate with the BS directly, which could not be affordable at long distances because they would deplete their battery much faster due to the nonlinear dependence of the power losses with the distance. Additionally, the configuration of the CHs should not be fixed and the nodes should take turns to undertake this function in order to balance the energy consumption of being a CH [4]. Thus, the hierarchy of CHs dynamically changes within the network. Clustering can be performed in different ways. For those in which CH sends the information directly to the BS (without relaying nodes), the clustering techniques are classified according to the activity performed by the BS. In this set, we distinguish the following clustering strategies:  
* Centralized Clustering. The BS has full control about how the clustering is performed. The BS always decides which nodes are converted into CHs. For this operation, the BS needs information about all the nodes in order to choose the most appropriate ones as CHs.