Implementation of Analytic Hierarchy Process in MATLAB

The implementation of Analytic Hierarchy Process (AHP) in MATLAB provides a convenient solution for mathematical modeling, particularly suitable for multi-criteria decision-making problems. The core workflow includes constructing judgment matrices, calculating weight vectors, and performing consistency checks.

Judgment matrix construction requires following the 1-9 scale method to reflect relative importance between factors. In MATLAB, matrix data can be directly input using two-dimensional arrays, with attention to maintaining the positive reciprocal property of the matrix. Code implementation typically involves creating a square matrix where each element a(i,j) represents the relative importance of element i over element j.

Weight calculation typically employs the eigenvector method. After calling the eig() function to solve for the matrix's largest eigenvalue and corresponding eigenvector, normalizing the eigenvector yields the weight distribution. The MATLAB implementation would involve: [V,D] = eig(matrix); max_eigenvalue = max(diag(D)); weight_vector = V(:,find(diag(D)==max_eigenvalue)); normalized_weights = weight_vector/sum(weight_vector);

Consistency check is achieved by calculating the CR value. MATLAB can automatically complete CI index calculation and RI table lookup comparison. If CR<0.1, the matrix passes the consistency test; otherwise, the judgment matrix needs adjustment. This process effectively avoids logical contradictions caused by subjective judgments. The implementation involves: CI = (max_eigenvalue - n)/(n-1); CR = CI/RI(n); where RI values are predefined based on matrix size.

For large-scale decision problems, the process can be encapsulated into function modules for automated calculation. Typical application scenarios include investment decisions, program evaluations, and other fields requiring quantitative comparisons. The modular approach allows for reusable code that can handle varying numbers of criteria and alternatives.