## 2 Cluster Head Selection
### Multi-Factor Evaluation Schemes
#### 2.3.1.1 Fuzzy Logic Controller
\begin{table}
\begin{tabular}{l l} \hline \hline
**Linguistic Parameters** & **Term Sets** \\ \hline
**Distance (D)** & Near, Moderate, Far \\
**Sensor Power (SP)** & Low, Moderate, High \\
**Network Traffic (NT)** & Light, Moderate, Heavy \\
**Probability of CH** & Very Weak, Weak, Little Weak, Medium, \\
**Selection (PCHS)** & Little Strong, Strong, Very Strong \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Linguistic parameters and their terms set. Figure 6: FLC structure. parameters. In [67, 68], the same authors of [66] replace the NT parameter with Degree of Number of Neighbour Nodes (D3N) as another important parameter for the selection of the CH. They evaluate the new proposed sets of parameters and compare the network performances such as network lifetime in [69]. The comparison of two fuzzy-based CH selection systems shows the better performance of the system with D3N as one of the inputs than the previous system. Although considering all the four factors [70] is the optimum solution, it can be concluded that the two parameters of remaining power of sensor nodes and number of neighbour nodes are more important parameters for the selection of CH than distance factor, accordingly. [PERSON] [71] introduces FLC for the CH selection phase to reduce the overhead of CH selection. Three fuzzy variables of energy, centrality and concentration of nodes are used to optimize the CH selection procedure and to prolong the network lifetime. As a centralized algorithm, BS collects the necessary information from all the nodes and applies the FLC rules to organize the clusters. The algorithm should address the issues of which other centralized algorithms face too. To enhance the network expansibility, a distributed Cluster Head Election mechanism using Fuzzy logic (CHEF) is offered by [72] as a contribution to [PERSON]'s algorithm [71]. The initial stage of the scheme is similar to LEACH algorithm, barring the threshold value P\({}_{\text{opt}}\), which is defined as a multiplication of the preferred number of CHs in LEACH by a constant value. According to the value of coefficient, a pool of candidate CHs are selected that each CH uses two fuzzy variables of energy and local distance to elect the optimal CHs. Unlike [PERSON]'s method, CHEF selects CHs in a localized method, which eliminates the overhead of collecting and calculating the fuzzy related information by the BS and ensures selection of one CH within r distance vicinity. However, the calculation cost of FL should be considered as a determinant factor for the exhaustible energy resources of sensor nodes, especially by increasing the number of input variables, which greatly increases fuzzy rules. Two-level fuzzy decision making is presented in [73], which provides the Local and Global level of decision making. In the local perspective, the algorithm focuses on the physical characteristics of sensor nodes such as internal energy and node degree. However, in the global perspective, network scale factors are considered to achieve balanced and optimized energy consumption. Hence a number of nodes are qualified at the local level by using energy level and number of neighbouring nodes as the input variables applied to local fuzzy system; and then selected candidates are re-evaluated at a global level, based on the parameters of centrality, proximity to the BS and distance between CHs. According to the simulation results presented by the paper, the proposed algorithm outperforms LEACH, [PERSON]'s method and CHEF in terms of network lifetime, residual energy of network and variance of energy in each round, although the complexity and overhead of two-level FL in implementation is not addressed by the paper. In [76], a Fuzzy Self Clustering Algorithm (FSCA) is proposed as a FL version of ACE [78].