# Optimizing Rule Weights to Improve FRBS Clustering in Wireless Sensor Networks
## 1 Introduction  
Nowadays, wireless sensor networks (WSNs) are experiencing increasing importance due to Internet of Things (IoT) applications [1], which gather information from a wide variety of environments, such as health monitoring [2], smart cities [3], industrial facilities [4], vehicles [5], greenhouses [6], etc. These WSNs are composed of tens or hundreds of small devices called nodes or motes [7]. These nodes have limited processing and storage capabilities due to the fact that they are usually isolated and battery powered, as well as needing a wireless interface to communicate to the base station or directly to the Internet through a gateway using, e.g., LoRaWan technology [8]. As commented previously, nodes are commonly powered with batteries because most WSN applications do not allow a power connection to the electric grid. Moreover, those batteries are usually difficult to recharge, so efficient resource management is required in every node, mainly when they have to send data, which is the most energy-demanding process in a node. Among the several techniques used in WSNs to achieve efficient resource managementmanagement (e.g., duty cycle scheduling [9] and data aggregation [10]), clustering appears one of the most important due to its capability to reduce the distance to send data [11]. Thus, with clustering it is possible to considerably decrease the energy spent in communications, and it can also be applied with other techniques like data aggregation. Clustering is based on the premise of selecting some nodes among the total of the WSN. These nodes are called cluster heads (CH) and they are selected based on an algorithm. The remaining nodes choose one of those CHs to send their data to them. After receiving information from normal nodes (e.g., temperature, humidity, gas concentration, etc. ), a CH aggregates these data and sends them to a base station (BS) or to a new layer of CHs when the network has a set hierarchy [11]. This process of selecting a set of CHs is commonly known as a _round_. A _round_ consists of selecting the CHs, gathering information from the nodes via the CHs, and the transmission of the data from the CHs to the BS. In centralized clustering methods, it is usual that the BS initiates each _round_, whereas in distributed methods this process usually requires some kind of scheduling, due to the lack of a common reference. Considering how clustering can be applied to the management of WSNs, it can be developed in several ways. Consequently, Figure 1 shows some of the most common approaches for clustering of WSNs. According to Figure 1, the first level in the classification takes into account how long the current selection of CHs is maintained. Thus, the _skip_ parameter defines how many _rounds_ will have the same CHs, avoiding the selection of these nodes in the second and ongoing rounds. Therefore, when the _skip_ parameter is greater than one, the whole network can save the energy of selecting CHs, which always requires sending new control messages. Thus, as far as _skip_ is concerned, most reviewed works renew the nodes that are selected as CHs each _round_; therefore, this is equivalent to employing a value of one for _skip_, so that new CHs are selected for each _round_[12]. Sometimes, the _skip_ value changes over time depending on the network conditions. In [13], the authors defined a _skip_ based on the output of a fuzzy controller. In [14], the authors proposed a semi-distributed method where the BS defines the _skip_ value, while the  
Figure 1: Clustering algorithm classification in WSN applications. CHs are selected by a fuzzy controller whose inputs are statistically normalized based on the data gathered from each node. A variable \(skip\) value was also computed in [15]. In this approach, nodes become CHs depending on prediction of the energy waste of being a CH. The next level in the taxonomy in Figure 1 refers to the exact point at which the decision of selecting a node as a CH is performed.