## 3 Performance Evaluation
### Experimental Details  
The CPU utilization evaluating process includes the following steps:  
1. Fuzzification of input RAM, physical disk values
2. Determination rules of application and method of inference
3. Defuzzification CPU utilization values  
Fuzzification of CPU utilization was performed using input variables and their membership functions of fuzzy sets. Results on the percentage of the utilization of RAM and storage, obtained from the input variables of the expert system based on fuzzy logic. Each input variable has three membership functions, that is, Gaussian membership functions were used in this proposed research paper. The fuzzy sets of input variables are listed in Table 3, and for both inputs (RAM and storage) the membership functions are shown in Figure 5.  
RAM and storage are two input variables. The output variable is the CPU utilization value that is defined by fuzzy logic, as shown in Figure 6. FIS accepts crisp input data, fuzzifies them, \begin{table}
\begin{tabular}{c c} \hline \hline
**Software and Hardware Components** & **Type and Capacity** \\ \hline Operating system & Windows 7 Enterprise, 64 bit \\ Hard-disk & 500 GB \\ Processor & 4 core, 3.10 GHz \\ RAM & 8.00 GB \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Testbed parameters. Figure 5: Membership function of RAM and storage. uses fuzzy on-premise operators (antecedent), implements inferences from the premise for output (sequential), combines the findings from fuzzy rules for creating a fuzzy inference and defuzzifies it to get a crisp conclusion. The proposed model in this paper is evaluated and tested using the Mamdani and Sugeno FIS. After defining inputs, the membership functions are constructed giving them ranges respectively. Membership functions are constructed to use in fuzzification and defuzzification. They map the non-fuzzy inputs to fuzzy values, which are then inferred according to the rule base. Figure 7 depicts the output variable with its member functions plotted on the curves. The three membership functions are mapped for each input data accordingly. Figure 6: Input and output variables: (**a**) Mamdani FIS model; (**b**) Sugeno FIS model. Figure 7: Construction of the output variable membership function of the Mamdani FIS model. The fuzzy rules editor is used to define the rules for the parameters being tested. The rules define the input and output membership functions that will be used in the output process. These rules are linguistic and also have a _\"IF-THEN\"_ form. Here the two parameters, RAM and storage, are linked through the _AND_ logical operation. These fuzzy set logical operations are used to perform the rules evaluation and then combining the results of the individual rules. Figure 8a shows the work of the inference engine of the Mamdani FIS. We defined nine rules for estimating CPU usage. In case several rules are active for the same output function of membership, it is necessary that only one value of membership is selected. This process is called \"fuzzy decision\" or \"fuzzy inference\". Several authors, including [PERSON], [PERSON], and [PERSON] developed a number of methods for fuzzy decision-making and fuzzy inference. The Mamdani FIS rules are generated using linguistic variables for both the premise and conclusion. The Mamdani FIS Model has established relationships between variables to evaluate the FIS model by highlighting fuzzy rules in terms used by a human expert in the form of IF-THEN [22]. The formula used for the centroids defuzzification method in the FIS Mamdani is as follows:  
\[Z=\frac{\int\mu_{c}(z)*zdz}{\int\mu_{c}(z)dz} \tag{4}\]  
The Sugeno FIS accepts a premise as a linguistic variable; however, its final part is a function, which can be zero (constant) or first order. The formula used by the Sugeno FIS for the weighted average defuzzification method is as follows [22]:  
\[Z=\frac{\sum\mu_{c}z*z}{\sum\mu_{c}z} \tag{5}\]  
The weights are determined by the learning process.