The industrial waste streams generated by mixed acid solutions contain concentrated solutions of toxic heavy metals, and improper disposal of these waste streams constitutes a significant factor in environmental problems when the metals are leached into the atmosphere. One approach to enhancing the recovery of critical metals involves using rational modeling and risk analysis to evaluate the processing options and identify the most economically efficient conditions to meet market demand, considering an environmentally friendly approach. Hence, this study sought to scrutinize the uncertainty impact of influential parameters on molybdenum efficiency during extraction and stripping stages from industrial effluent by employing a hybrid model that integrates the adaptive neuro-fuzzy inference system (ANFIS) with the particle swarm optimization (PSO) algorithm. The model was used to predict the operational conditions needed to achieve maximum efficiency while considering the presence of concentrated metal ions. The optimized model predicted that Mo removal from the waste solution could achieve 74.8 % under 20 min duration with the LIX 63 concentration of 24 % and equal O/A ratio at a temperature of 25 °C. Similarly, the mixing time, temperature, NaOH concentration, and A/O ratio for the recovery stage were determined to be optimized at 20 min, 25 °C, 2.0 M, and 0.6, respectively. Uncertainty of the predicted data was analyzed using Monte Carlo Simulation (MCS) and Latin Hypercube Sampling (LHS) for the removal and recovery stages. MCS revealed a 90 % confidence interval for removal (39.76–90.82 %) and recovery (63.06–91.08 %), with sensitivity analysis identifying the phase ratios as the most influential factors in both stages. The sodium molybdate specimen was obtained through crystallization from strip solutions and subsequently characterized using XRD and SEM-EDS analyses.