# Fuzzy-Logic Based Distributed Energy-Efficient Clustering Algorithm for Wireless Sensor Networks
## 2 Related Works  
LEACH (Low Energy Adaptive Clustering Hierarchy) is one of the most classical self-organizing adaptive clustering routing algorithms for WSNs in the early time, which averages the energy load of the whole network to each sensor node through regular CH election [13]. It can help to improve the scalability and robustness of dynamic networks to some extent. In the CH election stage, each node will generate a random number between 0 and 1. If this random number is less than the threshold \(T(n)\), the node will be elected as the CH node. The definition of \(T(n)\) is influenced by the parameters such as probability to be the CH, current round and the percentage of allowed CHs in the whole networks, which is shown as Equation (1). \[T(n)=\left\{ \begin{array}{ccc}\frac{p}{1-p[m\text{od}(1/p)]}&,&n\in G\\ 0&,&\textit{other}\end{array} \right. \tag{1}\]  
where \(p\) indicates the percentage of nodes to be CH during the election, \(r\) is the current CH election round and \(G\) is the set of nodes which fail to be selected as CH in the recent \(1/p\) rounds. Here the probability of each node to be CH is the same. After that, CHs allocate time slot to the member nodes in the cluster, and the data transmission within cluster will be performed with TDMA (Time Division Multiple Access) manner. Although LEACH is too ideal to fully consider the communication consumption in the actual transmission environment, and the randomness of CH election causes many deficiencies, LEACH provides a good theoretical basis and design model for the subsequent clustering algorithms. HEED (Hybrid and Energy-Efficient Distributed clustering approach) sets up a primary clustering parameter and a secondary clustering parameter during CH election as a measure of the cost of intra-cluster communication [14]. The primary parameter is dependent on the residual energy of the nodes and the nodes with higher residual energy will have a higher probability of being a CH. The secondary parameter reflects nodes proximity or the nodes density, which is used as an auxiliary indicator for the computation of communication cost within the cluster. This scheme builds clusters in a distributed way, extends the lifetime of the networks through minimizing the intra-cluster communication energy consumption, and keeps a good distribution for the CH nodes. Nevertheless, there are much more messages needed to be broadcast in the stage of cluster formation, which results in more additional system energy consumption. EADEEG (Energy-Aware Data Energy-Efficient Gathering protocol for wireless sensor networks) proposes an energy-efficient data gathering protocol based on cluster structure, which is also a kind of distributed clustering algorithm [15]. This scheme considers the node's energy and its neighbor nodes' energies simultaneously in CH election. It can reduce the energy consumption and prolong the lifetime of the networks to some extent. However, the scheme ignores the aspect of nodes degree, which might easily lead to isolated point problems in the networks. DSBCA (Distributed Self-organization in load-Balanced Clustering Algorithm for wireless sensor networks) defines the cluster radius threshold to achieve unequal clustering [16]. In CH election phase, new CH nodes are elected based on figuring out the weights determined by residual energy and node connectivity of each member node, which are evaluated by the former CHs. Although it could obtain the optimal CHs, the energy consumption of the network will be increased aggravatingly. EEREG (Energy Efficient Routing protocol based on Evolutionary Game theory) figures out the reasonable size of each cluster and the suitable CHs through game theory [17]. However, it is a kind of centralized algorithm with the awareness of the global topology of the networks, and also it will need higher requirements for the hardware of the sensor nodes.