# A New Centralized Clustering Algorithm for Wireless Sensor Networks
## 2 Related Work
Referred to as Cluster-head Election using Fuzzy Logic Algorithm (CHEF), it uses three input variables: energy, concentration and centrality. With a Fuzzy-I logic-based system, the output _chance_ models the appropriateness of a node to become a CH. An alternative algorithm is Energy-Efficient Distributed Clustering based on Fuzzy (EEDCF) [12]. In this distributed algorithm, the close nodes coordinate to determine the CHs from the chances computed by each node. This computation is based on a Fuzzy-I logic-based system. The proposal shown in [13], Type-2 Fuzzy Logic (Type2 FL), classifies the nodes in different levels according to their distance to the BS. Then, the best cluster is chosen using a Type-2 fuzzy system. A centralized method that uses the Type-2 Fuzzy logic is analysed in [14], named Clustering Routing Protocol for WSN Based on Type-2 Fuzzy Logic and Ant Colony Optimization (CRT2 FLACO). These techniques show that the use of the Type-2 Fuzzy logic improves the performance when compared with Type-I fuzzy logic systems. This improvement is due to the best management of the existing uncertainty, which is intrinsically present in this kind of network, as it is shown in the Cluster Head Enhanced Election Type-2 fuzzy Algorithm (CHETAH) [15] or Enhanced Unequal Distributed Type-2 Fuzzy Clustering Algorithm (EUDCF) in [5]. Hybrid clustering algorithms are also possible. In this kind of algorithm, both stochastic and fuzzy logic systems are employed to elect the CHs in the network. In this way, Fuzzy-based Hyper Round Policy Clustering Algorithm [16] starts choosing the CH in a stochastic way (based on residual energy) and later it uses a fuzzy system that establishes how many rounds each node is going to be as CH in a distributed way. From the studied bibliography, we have verified that centralized methods outperform the distributed ones. However, the works defining the centralized methods do not address how the information that the BS uses for the clustering is obtained. In particular, they commonly rely on residual energy and precise locations of the nodes. This implies that the nodes should be equipped with complex hardware (e.g., GPS), which could be a strong limitation in some WSN applications such as those in indoor infrastructures, subterranean environments or dense forests. Moreover, even in those applications where GPS is possible, its inclusion supposes an increment in the cost. In addition, most of the discussed papers do not provide a complete description about how some parameters (like coverage radius, transmission power of the advice message, etc.) are computed without inferring in additional control messages. We also concluded that Type-2 fuzzy systems are able to work with estimations better than Type-1 system. These estimations are necessary to reduce the control messages in real implementations. In this paper we present a detailed description of a novel centralized method without incurring in additional hardware costs for the nodes. The Base Station decides, based on a Type-2 fuzzy system with data gathered from the wireless sensor network, which nodes are going to be CHs while setting an optimised skip. In contrast to the previous works, this method introduces a new scoring method for selecting CHs in a WSN based on a Type-2 Fuzzy system. it was designed to allow that the same electedCHs can keep in their role for several rounds. That behaviour is based on the inertia of those types of networks and it is supposed, as was stated in the hypothesis H1, that several skipped rounds greater than 2 can prolong the network lifetime. In addition, due to the high uncertainty observed in this kind of problem, we propose the use of a Type-2 fuzzy system whose output interval can give further versatility and adaptability to different networks layouts. The description about how the input parameters of the fuzzy system are computed is included in the next Section.