Modification High Performance Training Algorithms for Solving Fuzzy Perturbed Integro-Differential Equations

Abstract

 In this pepear we develop a type of high-performance algorithm called a Quasi–Newton type training algorithm by designing a partial fuzzy neural network with fuzzy weights using the $\omega$-cut representation, and real biases (PFNN).Developing feed forward neural networks (FFNNs) to solve fuzzy singular perturbed Fredholm Integro-Differential Equations  (FSPFI-DEs) is the main goal of this paper. Modified Quasi-Newton training algorithm (QN)  of this design called the Fuzzy $\omega$ -cut Quasi–Newton (F $\omega$ QN) algorithm, and transfer function is each unit's sigmoid activation.To support the effectiveness and precision of our approach, a comparison between the outcomes of numerical experiments and the analytical solutions of a few examples has been conducted.