# Optimization of Clustering in Wireless Sensor Networks: Techniques and Protocols
## 6 Recent Advancements in Clustering Optimization Algorithms
### Fuzzy Logic  
Fuzzy logic was invented as a mathematical discipline for expression of approximate human reasoning. It allows for a measure of uncertainty or imprecision associated with the use of linguistic variables such as \"most, many, frequently\" through rules within a set called a fuzzy set [100]. In this section, fuzzy logic techniques were discussed and evaluated based on the fuzzy logic standard parameters and optimization process used (methodology and feature). To showcase a general outline of the different approaches, the comparison of techniques presented in Table 5.  
* DFCR: Distributed fuzzy approach to unequal clustering and routing algorithm The DFCR [79] was presented as an algorithm with four major steps: sharing of information, formation of clusters, formation of the virtual backbone, and routing of data. During the information sharing phase, the distances of each node from the BS and its neighbors are disseminated. Subsequently, the cluster formation step requires each node, in a distributed manner, to decide whether to become a CH by calculating its cluster radius using the local information. Each node in this algorithm computes its energy level and distance from the BS as the fuzzy input parameters for obtaining the competency function 1 (CF1) for selection as CH. At this point, each node's latency is calculated based on the obtained CF1. Upon expiration of the timer, the node radius is calculated based on CF1 and the derived fuzzy output, considering the neighbor cost and density of the CF2 output. Hence, CF1 and CF2 are considered fuzzy inputs; the cluster radius is estimated as the fuzzy output within each node, and a node is expected to distribute a notification message if it becomes the CH. Nodes that receive the message before the expiration of the  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Ref** & **Algorithm** & **Optimization Methods** & **Objective** & **Optimization Process** & **Matrices** & **Simulation** \\ \hline \multirow{9}{*}{[79]} & \multirow{4}{*}{DFCR} & \multirow{4}{*}{ \begin{tabular}{c} Fuzzy logic-based \\ clustering protocol for CH \\ selection and computation \\ of the cluster radius; \\ fuzzy logic is applied to \\ handle different levels of \\ system uncertainties \\ Development of an entirely \\ distributed fuzzy \\ logic-based system to \\ determine the eligibility of \\ each node for being selected \\ as CH, based on two input \\ factors and application of \\ linear prediction \\ Handling the uncertainties \\ in WSNs using fuzzy logic; \\ the algorithm considers \\ residual energy levels and \\ the distance to the BS \\ Fuzzy logic-based CH \\ nomination and \\ distribution control using \\ adaptive separation, which \\ is a fuzzy-based centralized \\ clustering method for \\ energy-efficient routing \\ frameworks in WSNs \\ CH selection using a \\ distributed fuzzy logic \\ engine algorithm wherein \\ the roles of the root nodes \\ are dynamically changed \\ based on their residual \\ energy levels \\ \hline \hline \end{tabular}  & \begin{tabular}{c} To reduce \\ energy use \\ deployment of mobile \\ gateways to establish \\ communication between \\ the CH and the BS \\ Selection of the final CHs \\ hotspot \\ problems \\ and balance \\ probabilistic model. \\ \end{tabular}  & \begin{tabular}{c} Number of dead \\ nodes, remaining \\ energy \\ \end{tabular}  & \begin{tabular}{c} OMNET++ \\ energy \\ \end{tabular}  \\ \hline \multirow{9}{*}{[81]} & \multirow{4}{*}{ \begin{tabular}{c} MOTCA \\ residual energy levels and \\ the distance to the BS \\ \end{tabular}  } & \multirow{4}{*}{ \begin{tabular}{c} To remove \\ hotspots \\ problems \\ and balance \\ probabilistic model. \\ \end{tabular}  } & \ \begin{tabular}{c} Selection of the final CHs \\ based on the energy levels \\ of the CHs are \\ nodeless, energy \\ depletion \\ \end{tabular}  & \begin{tabular}{c} Number of live \\ nodes, energy \\ depletion \\ \end{tabular}  \\ \cline{1-1}  & & & & \\ \cline{1 time will cease competing to be the CH.