aspg-21-2832-1791472201 20261008151001 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 24 3 Raed Hatamleh Department of Mathematics, Faculty of Science and Information Technology, Jadara University, P.O. Box 733, Irbid 21110, Jordan Uryson's operators are very famous in the theory of fuzzy functional analysis. This paper is dedicated to studying and generalizing many results about the compactness and the continuity of Uryson's operator in two-variables defined with integral equation on G with the norm ‖u‖f= sup(ρ(v,f)≤) |∫u(x)v(x)dxG | ;v(x)∈L*g ,u(x)∈Lf*. Also, we study the convergence of Urysons' sequences Kn defined with the family of functions Kn (x, y; u) by using the convergence with respect to the defined measure and Caratheodory Condition. 2024 233 239 2832 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.240320 https://www.americaspg.com/journal/21/article/2832 https://www.americaspg.com/storage/71716650411.pdf