Fuzzy Analytic Hierarchy Process with MATLAB Implementation

When implementing the Fuzzy Analytic Hierarchy Process (FAHP), the following systematic approach is recommended: First, identify and collect all relevant factors and criteria involved in the problem domain. This initial data gathering phase is crucial for building an accurate model. Next, construct a hierarchical structure model by organizing factors and criteria into different levels based on their relative importance. In MATLAB implementation, this hierarchy can be represented using nested cell arrays or custom class structures to maintain clear parent-child relationships between levels. For each level within the hierarchy, establish pairwise comparison matrices. These matrices capture the fuzzy judgments between elements. Implementation typically involves creating triangular fuzzy numbers (TFNs) using MATLAB's matrix operations, where each comparison is represented as (l, m, u) values denoting the lower, most likely, and upper bounds of the fuzzy judgment. Calculate the weight vectors for each factor and criterion. This step involves fuzzy arithmetic operations and normalization procedures. The MATLAB implementation may utilize eigenvalue methods or logarithmic least squares approaches, with functions like `eig()` for eigenvalue calculations and custom normalization routines to ensure weights sum to unity. Compute consistency indices for all factors and criteria to validate model stability. The MATLAB code should include consistency ratio calculations comparing the consistency index with random indices, typically implementing a check where CR < 0.1 indicates acceptable consistency. This can be achieved through functions that calculate the maximum eigenvalue and corresponding consistency metrics. Perform sensitivity analysis to evaluate model reliability and robustness. This involves systematically varying input parameters and observing output changes. In MATLAB, this can be implemented using parameter sweep algorithms and visualization tools like `plot3` or `mesh` functions to display how weight variations affect the final rankings. This implementation process requires solid mathematical foundations and programming expertise, particularly familiarity with MATLAB's matrix operations, fuzzy logic toolbox, and custom function development. Users unfamiliar with these technologies are advised to first acquire relevant mathematical and programming knowledge or seek assistance from experienced practitioners. The code structure typically involves main driver scripts, separate functions for matrix operations, consistency checks, and visualization modules to ensure modularity and maintainability.