aspg-33-2388-1792223556 20261017075236 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 2023 10 1 Mohammad Abobala Department of Mathematics, Faculty of Sciences, Tishreen University, Syria Despite the great and rapid progress in the study of Fuzzy Logic and its applications in various scientific fields, it has not yet been used to build a consistent number theory like classical number theory. This research provides for the first time a conception of the concepts of number theory based on fuzzy logic and fuzzy membership functions, where it defines the division process, the fuzzy congruence, the greatest common divisor between integers with a fuzzy membership function. On the other hand, it presents many famous Diophantine equations formulated using fuzzy sets, in addition to many properties of fuzzy number theoretical systems, through many related theorems and accompanying illustrative examples. Also, in this research, we are raising many open research questions related to fuzzy number theory, which we believe will represent the future of progress in the study of this new mathematical branch. 2023 17 25 2388 https://creativecommons.org/licenses/by/4.0/ 10.54216/GJMSA.0100102 https://americaspg.com/journal/33/article/2388 https://americaspg.com/storage/81704498744.pdf