MATLAB Implementation of the Analytic Hierarchy Process (AHP) Methodology

The Analytic Hierarchy Process (AHP) is a systematic decision-making analysis method that decomposes complex problems into hierarchical structures and quantifies the relative importance of various factors to support decision-making. MATLAB, as a powerful numerical computation tool, is highly suitable for implementing the AHP algorithmic workflow. The core steps of the Analytic Hierarchy Process include: constructing a hierarchical structure model, building judgment matrices, calculating weight vectors, and performing consistency checks. When implementing in MATLAB, the first step involves collecting expert pairwise comparison results for different factors to construct judgment matrices. Subsequently, the eigenvalue method can be employed to solve for the matrix's maximum eigenvalue and its corresponding eigenvector - this eigenvector represents the weight distribution among factors. To ensure the rationality of judgment matrices, consistency verification is essential. The consistency ratio (CR) is calculated, and if CR < 0.1, the judgment matrix is considered to have acceptable consistency; otherwise, the comparison results need readjustment. Key MATLAB implementation aspects include: - Using matrix operations for efficient pairwise comparison data organization - Implementing eigenvalue decomposition via the eig() function to obtain principal eigenvectors - Calculating consistency index (CI) using (λmax - n)/(n - 1) formula - Automating CR calculation through random index (RI) reference tables Implementing AHP through MATLAB enables efficient handling of complex weight calculation problems, making it applicable across various fields including engineering evaluation and economic decision-making. This methodology effectively combines subjective judgments with mathematical computations, rendering the decision-making process more scientific and transparent.