Hierarchical Analysis Code Implementation

The Analytic Hierarchy Process (AHP) is a widely-used decision-making analysis method applicable to solving various related problems. This approach breaks down complex problems into multiple hierarchical levels or factors, compares these factors through pairwise comparisons, and assigns weights to derive final decisions or solutions. AHP not only helps decision-makers decompose problems into smaller components but also ensures that final decisions align with practical requirements through systematic evaluation and weighting of each factor. In code implementation, AHP typically involves creating a comparison matrix where elements represent the relative importance between factors. The implementation calculates eigenvalues and eigenvectors to determine factor weights, followed by consistency ratio validation using the formula CR = CI/RI to ensure logical consistency in judgments. Key functions include matrix normalization, priority vector calculation, and consistency verification algorithms. Practical coding approaches often utilize numerical computing libraries for matrix operations and incorporate validation checks for comparison matrix integrity.