Integrating uncertainty and sentiment into the bass model for forecasting the diffusion of new energy vehicles

Forecasting the diffusion of new products is critical for production planning, marketing strategy, and managerial decision-making. The classic Bass diffusion model, while widely adopted, assumes a constant imitation coefficient and a deterministic framework, which limits its ability to capture the dynamic influence of consumer sentiment and the inherent uncertainty in real-world markets. To address these limitations, this study proposes an uncertain emotional Bass model that integrates uncertainty theory and sentiment analysis into the classic Bass framework. Specifically, an enhanced sentiment dictionary incorporating degree adverbs, negation words, and transition words is constructed, and a soft voting ensemble model combining Logistic Regression, Random Forest, XGBoost, and Naive Bayes is employed to extract a time-varying sentiment index from online reviews, which is then linked to the imitation coefficient through an S-curve function. Meanwhile, a Liu process-based uncertain noise term is introduced to characterize market uncertainty, transforming the model into an uncertain differential equation from which the α -path of cumulative sales and the uncertainty distribution of the first hitting time are derived. The proposed model is empirically validated using monthly sales data and 14,005 online reviews of the BYD Song Plus EV from October 2021 to February 2025. Results show that the model achieves a MAPE of 2.29% on the testing set, a 41.56% reduction compared to the standard Bass model (3.92%), while R 2 improves from 0.891 to 0.955 and prediction efficiency increases by 1.70%. The product lifecycle is estimated to end at approximately month 179 (February 2039), with a total market potential of about 2,139,812 units, and the median first hitting time for 2,000,000 cumulative sales is month 138 (April 2033). Scenario analysis reveals that cumulative sales forecasts at month 53 range from 495,833 units under pessimistic sentiment to 503,302 units under optimistic sentiment. These findings demonstrate that incorporating sentiment dynamics and uncertainty theory into diffusion modeling not only enhances forecasting accuracy and robustness but also provides managers with scenario-based decision support tools for production planning, risk assessment, and consumer sentiment management in the new energy vehicle market.