## 2 Cluster Head Selection
### Multi-Factor Evaluation Schemes
#### 2.3.1.1 Fuzzy Logic Controller  
The authors of [66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76] propose CH selection algorithm based on Fuzzy Logic (FL). FL is a problem-solving control system methodology that provides a simple way to arrive at a definite conclusion based upon a descriptive language to deal with input data more like a human operator. The following compatible features of FL with characteristics of sensor networks make it an apt solution to be implemented in CH selection stage:  
* Smooth noise-tolerant output control function in presence of wide range of input variations. * Adaptive modifiable governing rules for FL controller processes. * Simple and imprecise implementation of FL keeps the overall system cost and complexity low. * Reasonable number of inputs can be applied to FL controller. The basic elements of FLC, shown in Figure 6, are fuzzifier, inference engine, Fuzzy Rule Base (FRB) and defuzzifier. The process of decision-making is performed in four steps: \begin{table}
\begin{tabular}{c c} \hline \hline
**Number Rating** & **Verbal Judgment of Preferences** \\ \hline
**1** & Equally preferred \\
**3** & Moderately preferred \\
**5** & Strongly preferred \\
**7** & Very strongly preferred \\
**9** & Extremely preferred \\
**2, 4, 6, 8 indicate the medium value of above pairwise comparison.** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: A fundamental 1 to 9 scale. Figure 5: A simple AHP hierarchy consisting of three sample nodes. * Fuzzification of the input variables: taking the crisp inputs from each of them and determining the degree to which the inputs belong to each of the appropriate fuzzy sets. * Rule evaluation: taking the fuzzified inputs, and applying them to the antecedents of the fuzzy rules. It is then applied to the consequent membership function. * Aggregation of the rule outputs: the process of unification of the outputs of all rules. * Defuzzification: the input for the defuzzification process is the aggregate output fuzzy set chance and the output is a single crisp number. To control FL inputs, fuzzy variables should be defined at the outset. Fuzzy variables are considered as linguistic objects or words rather than the numbers. Each linguistic value is characterized by a label and a semantic value. Triangular and trapezoidal are two common shapes used as input membership functions. Membership function associates a weighting with each of the inputs that are processed; the function also defines functional overlap between inputs and ultimately determines an output response. The rules use the input membership values as weighting factors to determine their influence on the fuzzy output sets of the final output conclusion. Once the functions are inferred, scaled, and combined, they are defuzzified into a crisp output which drives the system. Most of CH selection algorithms using FL adapt Mamdani Method [77] as fuzzy inference technique and Center of Gravity (COG) as defuzzifier approach, but they differ in their utilization of variant input parameters and also in the scope of application of FLC to a local or global perspective of the CH selection process. In [66], distance of cluster centroid (D), remaining battery power of sensor (SP) and network traffic (NT) are defined as three input linguistic parameters of FLC, while the probability of CH selection (PCHS) is the desired output parameter. The linguistic parameters are defined in Table 3.  
The number of linguistic term sets of each parameter is 3; as a result the FRB has 27 rules. According to the paper, the simulations shows higher changes of PCHS by variation of SP input, which means greater importance of remaining battery power of a sensor for the selection of a CH than the two other