An integrated TOPSIS framework with Full-Range Weight Sensitivity Analysis for robust decision analysis

Abstract

Multi-criteria decision-making (MCDM) is widely used in engineering to assist in the selection of the best alternative according to various criteria. Many MCDM methods rely on fixed weight assignments, limiting their ability to reflect uncertainties or variations in decision-maker preferences. This work shows a novel approach that integrates the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) with conventional one-at-a-time Weight Sensitivity Analysis (WSA) and, for the first time, introduces the Full-Range Weight Sensitivity Analysis (FRWSA). FRWSA enumerates all admissible weight vectors on a discretized simplex and summarizes robustness as dominance frequency, the share of the simplex for which an alternative ranks first. A wastewater treatment plant (WWTP) case study evaluating four different configurations illustrates the approach. Using FRWSA with step h = 0.05 (10 million weight combinations), configuration A2/O-D dominates 82.80% of the weight simplex, with UCT at 12.17%, A2/O-S at 4.94%, and BARD at 0.09%. Comparing with Monte Carlo sampling, FRWSA provides a deterministic, variance-free baseline: MC–Dirichlet with $\alpha =0.5$ is nearly identical (JSD $\approx$ 0.001 bits), $\alpha =1.0$ is close but distinct (JSD $\approx$ 0.007-0.008 bits), and plain MC remains farther (JSD $\approx$ 0.043 bits) over 10⁴ – 10⁷ draws. The framework improves transparency via global coverage and boundary diagnostics and is method-agnostic (replicated with VIKOR in the SI). A reusable MATLAB implementation is provided to facilitate adoption. This integrated analysis supports robust and transparent engineering decisions wherever weight uncertainty matters.