# Multi-Objective Service Placement Scheme Based on Fuzzy-AHP System for Distributed Cloud Computing
## 3 Proposed Method
### Steps of the Proposed Scheme  
We propose an efficient placement scheme considering the metric. We propose an efficient placement scheme considering the metric. In steps 1 and 2, we gather information based on requirements and the resource state for SP. In steps 3 to 7, a fuzzy system is conducted for the SP decision. Then an AHP system is conducted in steps 8 to 10 for target machine selection. As shown in Figure 4, the detailed steps for the proposed SP scheme are as follows. * _Step 1. Resource monitoring and profiling_. The first step is to monitor the resource state of an ongoing service. It is needed for monitoring and profiling the SP decision and selecting the target machine. * _Step 2. Service requirement analysis._ Based on the demand of the user requirement, we categorize objectives and needed metrics. * _Step 3. Establish a fuzzy variable (create a membership function (MF))._ The concept of a fuzzy system is based on steps 3 to 5: fuzzification, rule construction and evaluation, and defuzzification [24]. The MF is used to calculate the probability values of an alternative for selecting the target machine. The input metric for the alternative is sent to the fuzzification phase in the fuzzy system, as shown in Figure 6.
* _Step 4. Fuzzy inference (rule construction)._ Rules are designed by the importance of the metric relationship. Algorithm 1 represents our Fuzzy block with fuzzify and defuzzify to set MF. * _Step 5. Defuzzifying._ In this step, we can obtain the output value of the \"Placement decision\" and \"Target machine list\" through the defuzzifying process. * _Step 6. Placement decision._ In the configuring system, through the configuration of rules, we obtain a more objective decision value. In this step, if the \"placement decision\" is detected, we go to the AHP system. * _Step 7. Perform the AHP system._ We construct the hierarchy structure based on AHP. AHP is an MCDM approach that can be used to solve complex decision problems. The main steps of AHP include making a hierarchy, assigning weights to each metric, investigating the consistency check of the system, and, ultimately, making a decision (determining the priorities of options). To select a service, this phase is the most important step. In this paper, we considered one scenario for energy and performance. A hierarchy structure of the performance metric is designed, as shown in Figure 5, based on previous approaches. * _Step 8. Determine the decision table._ We explain how to measure the decision. When an efficient SP scheme is applied, Table 6 defines the relative value for the policies based on Table 7. According to the relative value, we can calculate the weight. Figure 3: Service placement architecture. * _Step 9. Calculate the weight for metric._ We use a ranking method by priority. A ranking is a numerical scale of the numbers that indicate how many numbers are more important with respect to the metric to which they are compared. We use the standard Saaty AHP 9-level scales, as shown in Table 6. In this system, we have to perform a comparison of every combination of two VMs at the same level (pairwise comparison) so that it is stated mathematically. The evaluation begins with the metric that represents the delimitation of the trade-off. We also use the S (Score) as the example  
Figure 4: Proposed SP steps. to represent how the weight is defined. As shown in Table 8, thus, we get the matrix-based Equations (1)-(3). \[W_{m}=\sum W_{n} \tag{1}\]  
\[Wn=\frac{V_{n-1}}{Vn} \tag{2}\]  
\[\text{s.t}\max\sum W_{m} \tag{3}\]  
Figure 5: Hierarchical structure. Figure 6: Fuzzy system. \begin{table}
\begin{tabular}{c c} \hline \hline
**Relative Importance** & **Value** \\ \hline Equal importance & 1 \\ Somewhat more important & 3 \\ Definitely more important & 5 \\ Much more important & 7 \\ Extremely important & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Relative value. Table 6 defines relative score-based policies. In addition, in Table 8, we present the used metric explanation.