MATLAB Implementation of Analytic Hierarchy Process (AHP) for Mathematical Modeling

The Analytic Hierarchy Process (AHP) in mathematical modeling is a method for solving complex decision-making problems. It enables systematic comparison and weighting among multiple factors, serving as a powerful tool for multi-criteria decision analysis. In practical applications, to effectively utilize the AHP methodology, we need to develop programs that can automatically execute the algorithm. MATLAB provides an ideal platform for implementing such programs due to its strong matrix computation capabilities and mathematical function libraries. A typical MATLAB implementation of AHP involves several key algorithmic steps: First, constructing pairwise comparison matrices using the 1-9 scale method to quantify relative importance between criteria. Second, calculating priority vectors through eigenvalue decomposition or approximation methods to determine weights. Third, performing consistency checks using the consistency ratio (CR) to ensure logical judgment consistency. Fourth, implementing hierarchical synthesis to compute final priority scores for decision alternatives. The programming implementation allows for automated calculation of weight vectors, consistency validation, and sensitivity analysis. Key MATLAB functions employed include 'eig' for eigenvalue computation, matrix operations for comparison matrix processing, and custom functions for consistency index calculation. Through programming the AHP algorithm, users can gain deeper understanding of the method's theoretical principles while facilitating efficient decision analysis through parameter customization and result visualization capabilities.