Modified Levenberg–Marquardt Training Algorithm for Solving Fuzzy Perturbed Integro-Differential Equations

الملخص

In this paper, will develops a high-performance training algorithm based on the
Levenberg–Marquardt (LM) algorithm by designing a partial fuzzy neural network
(PFNN) with fuzzy weights, expressed through the ω-cut representation, and real biases.
The main goal of this paper is to develop feedforward neural networks (FFNNs) for
solving fuzzy singularly perturbed (FSPFI-DEs). The modified Levenberg–Marquardt
(LM) algorithm designed for this purpose is called the Fuzzy ω-cut Levenberg–
Marquardt (F ωLM) algorithm, and the sigmoid function is used as the activation
(transfer) each unit's function. To demonstrate the effectiveness & precision of the
suggested method, the results of numerical experiments for several examples are
compared with the corresponding analytical solutions.