A Multilinear Model Interpretable by Multiplicative Coalitions for Medical Diagnosis: Application to COVID-19 Prediction in Pregnant Women

This work proposes the Multilinear Model by Multiplicative Coalitions (M2CM), an interpretable multicriteria method to support medical diagnosis. M2CM captures pair-to-pair interactions between symptoms through synergy and redundancy weights, estimated via quadratic programming with supervised data. The model preserves characteristics of the 2-additive version of the Choquet integral and relaxes its monotonicity constraints, making it more suitable for clinical contexts. The method was evaluated in the prediction of COVID-19 in pregnant women using real data from REBRACO (Brazilian Network of COVID-19 Studies in Obstetrics). In experiments with 1,001 random training and test partitions, M2CM showed performance comparable to machine learning models (Logistic Regression, XGBoost) and superior to classical multi-criteria methods (SAW, TOPSIS), with the advantage of offering native interpretability through the visualization of learned weights.