Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/2017 2022 2022 Islamic Online University, Department Of Science and Information Technology, Doha, Qatar Rama Rama Fuzzy logic plays a huge role in the symbolic inference and causality associated with modern cognitive human systems. In this paper, we present a mathematical method that defines the mechanism of forming a hybrid structure in which neural networks and expert systems are connected so that one forms a primary processing stage for the other, where the neural network can act as a primary processor that processes low-level information, or as an internal Subsystem for learning tasks or generalization and classification. Where neural networks can be used to generate rules using training data and then submit these rules to be used by a fuzzy system to give the final results. 2023 2023 18 25 10.54216/GJMSA.070102 https://www.americaspg.com/articleinfo/33/show/2017