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Rising market demands, economic pressures, and technological advancements have spurred researchers to seek ways to enhance business environments and scientific productivity. Predictive science, crucial in this context, has gained prominence due to the rapid progress in information technology and forecasting algorithms. Time series forecasting, widely used in fields like engineering, economics, tourism, and energy, has inherent limitations with classical statistical methods, leading researchers to explore artificial intelligence and fuzzy logic for more accurate predictions. However, despite extensive efforts to improve accuracy, challenges persist. The research introduces a model aimed at surpassing existing methods in time series forecasting accuracy. This approach combines meta-heuristic optimization algorithms and neutrosophic logic to enhance precision in uncertain and complex environments, promising improved forecasting outcomes. The study shows that the performance of the neutrosophic time series modeling approach is highly dependent on the optimal selection of the universe of discourse and its corresponding intervals. This study selects the quantum optimization algorithm (QOA), genetic algorithm (GA), and particle swarm optimization (PSO) to address this weakness. These optimization algorithms improve the performance of the NTS modeling approach by selecting the global universe of discourse and corresponding intervals from the list of locally optimal solutions. The proposed hybrid model (i.e., NTS-QOA model) is verified and validated with datasets of university enrollment of Alabama (USA), Taiwan futures exchange (TAIFEX) index, and Taiwan Stock Exchange Corporation (TSEC) weighted index. Various experimental results signified the efficiency of the proposed model over existing benchmark models in terms of average forecasting error rate (AFER). This value using the proposed NTS QOA, NTS GA, and NTS PSO method on the university dataset is 0.166, 0.167, 0.164, on the TAIFEX dataset, is 0.081, 0.081, and 0.081, and on the TSEC dataset is 0.09, 0.09, and 0.09, respectively. [ABSTRACT FROM AUTHOR]