# Binary Decision Support Using AHP: A Model for Alternative Analysis
## 2 The AHP Method  
Decision-makers often analyze complex systems with multiple interdependent components, such as resources, objectives, people, or organizations. [PERSON] developed the Analytic Hierarchy Process (AHP) in 1980, which provides a structured approach for evaluating multiple criteria in decision-making scenarios [19]. This method allows decision-makers to decompose complex problems into hierarchical structures, enhancing the clarity and facilitating comparisons. Researchers widely apply the AHP in engineering, economics, healthcare, and public policy because it integrates qualitative and quantitative criteria into a logical decision-making framework [20]. A more detailed explanation of the AHP begins by structuring the decision problem into a hierarchy, which typically includes three levels: the overall goal at the top, the criteria and subcriteria that define decision parameters in the middle, and the alternatives at the bottom. This hierarchical breakdown enables decision-makers to systematically analyze each problem component, enhancing the transparency and understanding [21]. Next, decision-makers perform pairwise comparisons, assessing the relative importance of each pair of elements within the same level (for example, comparing two criteria or two alternatives) using [PERSON]'s scale, which ranges from 1 (equal importance) to 9 (extreme importance) [22]. These comparisons form a pairwise comparison matrix, and mathematical methods, such as the principal eigenvector approach, derive the priority vectors (weights). The process culminates by synthesizing priorities via combining the weights of criteria and alternatives to identify the most suitable option. A sensitivity analysis also assesses the robustness of the decision [21]. At its core, the AHP relies on hierarchical structuring, where decision-makers divide a problem into three levels: the goal (or objective), the criteria and subcriteria, and the alternatives under comparison. Decision-makers perform pairwise comparisons of these elements using [PERSON]'s numerical scale, which ranges from 1 to 9 to indicate the relative importance of one aspect over another, as detailed in Table 1[23]. Figure 1 shows the hierarchical structure of the AHP and the logical arrangement of objectives, criteria, and decision alternatives. A key strength of the AHP lies in its ability to systematically handle subjectivity, as it allows experts to express preferences with a structured methodology. After performing pairwise comparisons, experts calculate the Consistency Ratio (CR) to assess whether the judgments remain logically coherent. In group decision-making contexts, researchers primarily aggregate individual pairwise comparisons into a group comparison using the Aggregation of Individual Judgments (AIJ) and Aggregation of Individual Priorities (AIP). In the AIJ method, researchers compute the geometric mean of the individual judgments for each pairwise comparison, which produces a combined comparison matrix that preserves the reciprocal property of AHP matrices. Researchers then use this aggregated matrix to derive group priorities. In the AIP method, each participant calculates their priority vector, and the group priority results from averaging these vectors, usually using the arithmetic mean [26]. The criteria in the AHP model play a critical role, so decision-makers should carefully define them according to the decision context. Typical criteria include financial factors (e.g., cost, return on investment), strategic factors (e.g., alignment with organizational goals), risk-related factors (e.g., operational, regulatory, reputational risks), stakeholder-centric factors (e.g., customer satisfaction, employee engagement), and technical factors (e.g., feasibility, resource availability). Decision-makers can further break down these criteria into subcriteria to enable a more granular and customized analysis, which ensures that they systematically consider all relevant aspects of the decision problem.