# Multi-Objective Service Placement Scheme Based on Fuzzy-AHP System for Distributed Cloud Computing
## 4 Evaluation
### Relation of Metric for Energy Efficiency
#### 4.2.2 Decision of Placement  
For the decision of placement, we use the fuzzy system. In this section, we represent the decision of placement using MF.  
* MF for the resource metric.  
Figure 7: WT/reliability trade-off.  
\begin{table}
\begin{tabular}{c l} \hline \hline
**Type** & **Value** \\ \hline CPU & Intel core i5-4690 3.50 GHz \\ RAM & 16 GB \\ \hline \multirow{3}{*}{CDC environment} & Number of CDCs 2 \\  & Number of hosts: 4 \\  & Number of VMs: 16 \\  & Number of cores: 2 \\  & Number of VM instance types: Small Instance: 1 EC2 Compute Unit, 1.6 GB *4 \\  & Number of services: 25 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Evaluation environment.  
\[\mathbf{F}=\mathbf{x},\mathbf{\mu}\mathbf{F}(\mathbf{x})\left|\mathbf{x}\in\mathbf{X}\right. \tag{11}\]  
At this step, metric values are mapped to the appropriate linguistic values by the corresponding universal set. For example, if \(\mathbf{X}\) is the universal set, then its elements are denoted by \(\mathbf{x}\), such that the fuzzy set F in \(\mathbf{X}\) is a set where \(\mathbf{\mu}\mathbf{F}(\mathbf{x})\) is an MF of x in F. This step maps each element of \(\mathbf{X}\) onto a value between 0 and 1 [25]. In this paper, we used MF to represent the fuzzy number. Based on the linguistic input value, the interface module selects the appropriate rule to be applied and produces the linguistic output value. Both the fuzzifier and defuzzifier use an MF to convert numerical values to linguistic values and vice versa. The MF maps each numerical value to a membership value (certainty level) between 0 and 1 (0 completely uncertain, 1 completely certain). Algorithm 1 describes our fuzzy block, which uses fuzzify and defuzzify techniques to determine the MF. Figures 8 and 9 show the results of Algorithm 1.  
In other words, to allow the fuzzy value to map for any metric configuration, we set the range for metrics such as CPU consumption to value between 0 and 1. The MFs for CPU consumption and RAM consumption are shown in Figure 8.  
As shown in Figure 8a, there are five rules ranging from low to high. We decided on an MF range from low to high. This represents essential parts for SP. In this step, the proposed scheme obtains more reliability than the existing model. The initial MF range is narrow, which is shown in Figure 8a. After configuring for MF, MF ranges of \"medium\" and \"mediumHigh\" are widened, as in Figure 8b. Through the proposed system, we can configure the fuzzy value. By fuzzy value configuring, we can obtain a more objective metric than the conventional fuzzy system in the decision step. The RU of cloud services changes dynamically. Because of uncertainty, it is difficult to satisfy user's requirements from the mathematical representation.  
Figure 8: MF for RU. (**a**) Initial MF. (**b**) MF after configuration.  
Figure 9: Fuzzy value range for decision of placement.  
To solve this limitation, we used a fuzzy system with a dynamically changed section. We called it a control point when the value of \"Necessity of Placement\" is detected. We present the fuzzy-value configuring stage in Figure 9.  
* MF for the decision of placement  
When \"Necessity of Placement\" is higher than the threshold, placement, or migration that occurs. Figure 8 shows the result of the MF decision of placement. The fuzzification stage maps an input metric to the appropriate MF. In the inference stage, we represent an appropriate if-then rule and make a result based on the rule.  
The output value converts the combined result back into a specific control output value. To transform the results into the output value, defuzzification is performed. In these processes, we used the center of gravity method, which is a common and useful defuzzification stage in fuzzy systems. Figure 8 represents MF for a result of the decision of placement.  
Through the output value, we can decide whether to perform the SP action.