Inclusion-exclusion integral neural network with monotone regularization terms

While deep learning has achieved significant success across various fields, the lack of transparency in decision-making remains a major challenge. To enhance interpretability, we propose an Inclusion-Exclusion Integral Neural Network (IEINN), a novel neural network model based on a non-linear integral defined with respect to a non-additive measure. This model is particularly suitable for systems where monotonic relationships exist between inputs and outputs. However, training without enforcing monotonicity constraints may lead to overfitting and difficulties in interpreting learned parameters. To address this, we introduce a monotonicity-preserving regularization term to ensure learned parameters remain consistent with non-additive measure theory. Experimental results across multiple datasets demonstrate that our approach enhances both model interpretability and predictive stability.