MATLAB Implementation of TOPSIS Method with Code Description

TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) is a widely used multi-criteria decision-making method that ranks alternatives by calculating their relative closeness to both the ideal and negative-ideal solutions. The MATLAB implementation typically involves the following computational steps: Data Normalization: Different dimensional indicators are normalized using methods such as vector normalization or min-max scaling. In MATLAB, this can be implemented using array operations and built-in functions like 'normalize' or custom standardization routines. Weighted Normalization Matrix: Apply weights to the normalized data based on indicator importance. This involves element-wise multiplication between the normalized decision matrix and the weight vector using MATLAB's array operations. Determine Ideal and Negative-Ideal Solutions: Identify the optimal and worst values for each criterion. The ideal solution consists of maximum values for benefit criteria and minimum values for cost criteria, which can be computed using 'max' and 'min' functions along matrix dimensions. Distance Calculation: Compute Euclidean distances from each alternative to both ideal solutions using vector norms or the 'pdist2' function. The calculation typically involves summing squared differences along each criterion dimension. Relative Closeness Calculation: Calculate the closeness coefficient using the formula C_i = D_neg_i / (D_ideal_i + D_neg_i), where values closer to 1 indicate better alternatives. This can be implemented through element-wise division and array operations. Comparison with Analytic Hierarchy Process (AHP): Methodology Principle: AHP constructs hierarchical structures and calculates weights from judgment matrices relying on expert inputs, while TOPSIS directly computes distances based on data without subjective judgment matrices. Application Scenarios: AHP suits decisions with clear hierarchical relationships among criteria, whereas TOPSIS works better for independent, data-driven multi-criteria ranking problems. Computational Complexity: AHP requires consistency checks making it computationally intensive, while TOPSIS has a streamlined workflow suitable for large-scale datasets. Both methods can be integrated, for instance using AHP to determine weights followed by TOPSIS for alternative ranking, creating a hybrid decision-support system implementable through combined MATLAB functions.