International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2618 2020 2020 An Effective Algorithm for Solving Weak Fuzzy Complex Diophantine Equations in Two Variables Applied Science Private University Amman,11931, Jordan Wael Wael Faculty of Information Technology, Abu Dhabi University, Abu Dhabi, UAE Wael Mahmoud M. Salameh Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Malik Bataineh Department of Mathematics, Jerash University, Jerash 26150, Jordan Mowafaq Omar Al Al-Qadri Department of Mathematics, College of Science and Art, AlUla branch, Taibah University, Medina, Saudi Arabia Ayman Alahmade Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, Jordan Abdallah Al Al-Husban Weak fuzzy complex numbers are defined as , with  as an extension of real numbers with . This paper is dedicated to studying weak fuzzy complex linear Diophantine equations in two weak fuzzy complex variables, by transforming the weak fuzzy complex Diophantine equation to a classical equivalent Diophantine system and going directly from the solutions of classical system into the desired equation. Algorithms for generating solutions of the previous equation will be presented in terms of theorems with many related examples that clarify the validity of our work. 2024 2024 386 394 10.54216/IJNS.230431 https://www.americaspg.com/articleinfo/21/show/2618