1. Introduction

2. Literature Review

3. Methodology

3.1. Analytic Hierarchy Process(AHP) Method

Analytic Hierarchy Process (AHP) is a multi-criteria decision-making method developed by Thomas L. Saaty in the United States. AHP is primarily used in decision-making processes that require complex and important judgments across various fields, and it has proven to be useful in decision-making related to corporate strategies or government policies as well. AHP decomposes decision problems into a hierarchical structure to derive priorities among relevant alternatives. Its application method is straightforward, allowing for easy expression of decision-making processes. Moreover, AHP can synthesize representative results from diverse judgments, thereby offering significant advantages by surveying experts related to the decision topic[15].

Setting up hierarchies for decision-making generally relies on literature reviews or expert opinions. The hierarchy structure typically includes Goal, Criteria, Sub-Criteria, and Alternatives. The Goal represents the objective of the decision-making process. Since the Goal guides respondents' judgments regarding the criteria and alternatives, it needs to be carefully and specifically defined by the surveyor. Criteria represent factors or attributes contributing to the Goal. The structure of Criteria forms the hierarchy, and pairwise comparisons among Criteria largely determine the significance of applying AHP in the decision-making process. Alternatives refer to the options or solutions targeted for decision-making through AHP[16].

Criteria forming the hierarchy undergo pairwise comparisons through surveys of experts, typically utilizing a 1-9 scale refer to table 1[x]. In pairwise comparisons, numbers from 1 to 9 reflect relative importance or preference between two factors (A and B), where 1 indicates equal importance, 3 slight preference, 5 moderate preference, 7 strong preference, and 9 extreme preferences. Closer to 9 signifies greater importance of the factor[16].

Table 6. Saaty’s 1-9 Point Scale.

Table 6. Saaty’s 1-9 Point Scale.

Scale	Definition	Description
1 3 5 7 9	Equally important A bit important Quite important Great important Absolutely important	If two elements are judged to be equally important. If one element is slightly more important than the other. If one element is significantly different from the other. If one element is definitely important than the other. If one element is deemed absolutely more important than the other.

The interpretation of the above scale is known as pairwise comparison, which means comparing two entities at a time to select relatively preferred or important ones. AHP enhances the accuracy of human judgments by repeatedly conducting such pairwise comparisons. The results of multiple pairwise comparisons can be summarized into a pairwise comparison matrix. The pairwise comparison matrix is a square matrix with the same number of rows and columns, as shown in Equation 1[16].

$$A=\left[\begin{array}{ccc}1& \begin{array}{cc}{a}_{12}& \cdots \end{array}& a_{1n}\\ \begin{array}{c}{a}_{11}\\ ⋮\end{array}& \begin{array}{cc}1& \cdots \\ ⋮& \cdots \end{array}& \begin{array}{c}{a}_{2n}\\ ⋮\end{array}\\ a_{n1}& \begin{array}{cc}{a}_{n2}& \cdots \end{array}& 1\end{array}\right]$$

$$a_{ij}=1/a_{ji}{a}_{ii}=1$$

(1)

Once the comparisons of criteria are completed on the questionnaire, AHP calculates the priority or weights of each element through mathematical processes. The applied equation for deriving the relative weights of decision factors is given as Equation (2), where ${\omega }_i$ represents the relative importance of the 𝑖th evaluation factor, and when evaluating factor 𝑖 is pairwise compared with another evaluation factor 𝑗, the importance is denoted by ${\omega }_{ij}$. The relative importance is derived from the pairwise comparison matrix using the Eigenvalue method, as shown in Equation (3)[16].

$$A=[a_{\mathrm{i}\mathrm{j}}]=\left[\begin{array}{ccc}{\omega }_1/{\omega }_1& \begin{array}{cc}{\omega }_1/{\omega }_2& \cdots \end{array}& {\omega }_1/{\omega }_{\mathrm{n}}\\ \begin{array}{c}{\omega }_2/{\omega }_1\\ ⋮\end{array}& \begin{array}{cc}{\omega }_2/{\omega }_2& \cdots \\ ⋮& \cdots \end{array}& \begin{array}{c}{\omega }_2/{\omega }_{\mathrm{n}}\\ ⋮\end{array}\\ {\omega }_{\mathrm{n}}/{\omega }_1& \begin{array}{cc}{\omega }_{\mathrm{n}}/{\omega }_2& \cdots \end{array}& {\omega }_{\mathrm{n}}/{\omega }_{\mathrm{n}}\end{array}\right]$$

(2)

$$A·\omega ={\lambda }_{max}·\omega$$

(3)

The pairwise comparison method assesses the consistency of comparison matrices to judge the reliability of the results. To do this, it calculates the Eigenvector and Eigenvalue of the comparison matrix, and computes the Consistency Index (CI) and Consistency Ratio (CR). The Consistency Ratio is calculated by dividing the Consistency Index by the consistency of a random matrix and is used to obtain more consistent comparison results. Particularly in real survey responses, there may be inconsistencies, so measuring the degree of consistency is necessary. CI and CR can be defined using Equations (4) and (5)[16]. RI stands for Random Index, which represents the consistency index when a pairwise comparison matrix is randomly generated using a random scale. The consistency index is calculated based on the size of the matrix.

$$CI=\frac{{\lambda }_{max}-n}{n-1}$$

(4)

$$CR=\frac{CI}{RI}$$

(5)

If the CR is 0, it means that the respondent conducted pairwise comparisons consistently. Generally, when the CR is within a maximum of 0.1 or 0.2, the pairwise comparison matrix is considered consistent. A CR within 0.2 is deemed an acceptable level of consistency, while a CR above 0.2 indicates insufficient consistency and suggests the need for reassessment[16].

4. Result

5. Conclusion

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