An Effective Algorithm for Solving Weak Fuzzy Complex Diophantine Equations in Two Variables

Mayada Abualhomos¹, Wael Mahmoud M. Salameh^2,*, Malik Bataineh³, Mowafaq Omar Al-Qadri⁴, Ayman Alahmade⁵, Abdallah Al-Husban⁶

^1.Applied Science Private University Amman,11931, Jordan,

²Faculty of Information Technology, Abu Dhabi University, Abu Dhabi, UAE

³Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan

⁴Department of Mathematics, Jerash University, Jerash 26150, Jordan

⁵Department of Mathematics, College of Science and Art, AlUla branch, Taibah University, Medina, Saudi Arabia

⁶Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, Jordan

Emails: abuhomos@asu.edu.jo; wael.salameh@adu.ac.ae; msbataineh@just.edu.jo; m.alqadri@jpu.edu.jo; aaahmdi@taibahu.edu.sa; dralhosban@inu.edu.jo

Abstract

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.

Keywords: Weak fuzzy complex integer; Diophantine system