MATLAB Implementation of TOPSIS Method with Comparison to Analytic Hierarchy Process

In MATLAB, both TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and Analytic Hierarchy Process (AHP) serve as decision analysis tools. While both methods address similar problem domains, they exhibit distinct differences in methodology and application scenarios. The TOPSIS method typically handles decision problems involving multiple competing alternatives that require evaluation and ranking. This ranking is determined by calculating the relative distances between each alternative and both the ideal solution and negative-ideal solution. The core algorithm involves normalizing decision matrices, weighting criteria, and computing separation measures using Euclidean distance calculations. MATLAB implementation typically requires functions for matrix normalization, weight assignment, and distance computation, often utilizing built-in functions like 'pdist' or custom vector operations. The key advantage of TOPSIS lies in its ability to handle data uncertainty and fuzziness through appropriate normalization techniques. However, a significant limitation is the requirement for predetermined criterion weights, which can be implemented using either equal weighting or expert-defined weight vectors. In contrast, Analytic Hierarchy Process (AHP) provides a structured approach for analyzing multi-criteria decision problems by decomposing them into hierarchical structures and quantifying the importance of each factor. The method employs pairwise comparisons to establish priority matrices and calculates consistency ratios to validate judgment coherence. MATLAB implementation of AHP typically involves creating comparison matrices, computing eigenvectors for priority weights, and verifying consistency using the consistency index (CI) and consistency ratio (CR) calculations. The principal advantage of AHP is its capability to handle complex multi-criteria decisions without requiring prior knowledge, through systematic pairwise comparisons. However, the method demands substantial computational effort for matrix operations and consistency checks, making it more time-consuming than TOPSIS in MATLAB environments. Therefore, while both methods are viable for decision analysis, the choice between TOPSIS and AHP in practice depends on specific circumstances and problem characteristics, including data availability, computational resources, and decision complexity.