Smoking-induced non-communicable diseases (SiNCDs) pose a serious global public health challenge and require effective and interpretable predictive models for early risk assessment. In this study, we propose an efficient Partially Interpretable Adaptive Softmax (PIA-Soft) model to predict the risk of developing SiNCDs while maintaining model interpretability. The proposed model integrates a linear component to capture the fundamental relationship between input variables and disease outcomes, and a non-linear neural network component to model complex feature interactions, thereby improving predictive performance. The proposed PIA-Soft model is evaluated using the Korea National Health and Nutrition Examination Survey (KNHANES) dataset and compared with several excellent machine learning models. Experimental results demonstrate that the PIA-Soft model achieves superior performance, with an accuracy of 0.841 and an F-score of 0.836. Moreover, the model provides partial interpretability by quantifying the contribution of individual features to the prediction outcome, which is important for medical decision-making. The results indicate that the PIA-Soft model is an interpretable and effective approach for predicting smoking-induced non-communicable diseases and has strong potential for supporting clinical and public health applications.