Solving intuitionistic fuzzy integro-differential equations using artificial neural networks and newton-cotes methods

In this paper, a modified method based on artificial neural network and Newton-Cotes methods with positive coefficients was developed and applied for the first time in the literature to solve the intuitionistic fuzzy integro-differential equations (IFFIDEs), where the parameters and variables are considered intuitionistic fuzzy numbers. The triangular intuitionistic fuzzy number (TIFN) was used for expressing intuitionistic fuzzy variables and parameters. The fuzzification of the deterministic r-cut and β-cut solutions leads to the artificial neural intuitionistic numerical solution. The main reason for using neural networks is their applicability in handling the intuitionistic fuzzy variables and parameters of IFFIDEs. A numerical example was given to demonstrate the proposed method. The results agree with the theoretical prediction and highlight how the combination of artificial neural networks and Newton-Cotes method enhances the accuracy and efficiency of solving IFFIDEs, making our proposed method valuable for application in fields such as engineering, medicine, and physics.