Scalable TOPSIS Variants in Web-Based Decision Support Systems: A Performance Benchmarking Study on Vectorization and Uncertainty Modelling

This study systematically benchmarks the computational performance and decision consistency of three TOPSIS variants—classical TOPSIS, vectorized TOPSIS, and Z-TOPSIS—in scalable web-based multi-criteria decision support systems (DSS). Although TOPSIS is widely used due to its simplicity and interpretability, its scalability and computational behavior under concurrent web workloads remain insufficiently explored. To address this gap, the algorithms were evaluated using datasets containing 50–500 alternatives and 10 criteria, representing realistic decision-making scenarios. Classical TOPSIS was used as the baseline, vectorized TOPSIS applied matrix-based optimization, and Z-TOPSIS incorporated Z-numbers to capture uncertainty. Experiments were conducted on a cloud-based DSS equipped with multi-core CPUs and 16–32 GB RAM, measuring execution time, throughput, response time, and ranking consistency under workloads of 50–500 concurrent users. The results show that vectorized TOPSIS reduced execution time by approximately 50–55% (26.3 ms vs. 57.9 ms) and achieved the highest throughput of 480 requests per second. In contrast, Z-TOPSIS produced higher latency (68.4 ms) due to additional reliability computations. Ranking consistency remained high between classical and vectorized TOPSIS (Kendall’s tau ≥ 0.98), while Z-TOPSIS showed minor deviations (tau = 0.91). These findings provide practical guidance for selecting TOPSIS variants in scalable web-based MCDM applications.