A Novel Hybrid ANFIS-NARX and NARX- ANN models to Predict the profitability of Egyptian Insurance Companies

The use of fuzzy logic models with machine learning (ML) models have become common in many areas, especially insurance field. This study aims to compare between non-hybrid models such as artificial neural network (ANN) model, adaptive neural fuzzy inference system (ANFIS) model, nonlinear auto-regressive external input (NARX) model, and the following hybrid models (ANFIS-NARX) and (NARX-ANN) to predict the profits of the insurance activity which represent the important indicator of the good performance of Egypt's 39 insurance companies in the period from 1st January 2009 to 31 December 2022 , monthly .This prediction based on the following factors (net premiums, reinsurance commissions, net income from earmarked investments, other direct income, net compensation, production cost commissions and general and administrative expenses) that help decision makers to make appropriate decisions . The results found that the (ANN) model is given good results compared with the following models (ANFIS), (NARX), hybrid (ANFIS-NARX) and (NARX-ANN) models according to the following prediction accuracy measures (RMSE, MAPE, MAE and Theil inequality). The explanatory ability (R2) was appeared (0.79, 0.61) respectively for training and testing phases in persons insurance companies. The explanatory ability also was appeared (0.83, 0.68) respectively in property insurance companies.