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International Journal of Neutrosophic Science
Volume 23 , Issue 4, PP: 386-394 , 2024 | Cite this article as | XML | Html |PDF

Title

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

  Mayada Abualhomos 1 ,   Wael Mahmoud M. Salameh 2 * ,   Malik Bataineh 3 ,   Mowafaq Omar Al-Qadri 4 ,   Ayman Alahmade 5 ,   Abdallah Al-Husban 6

1  Applied Science Private University Amman,11931, Jordan
    (abuhomos@asu.edu.jo)

2  Faculty of Information Technology, Abu Dhabi University, Abu Dhabi, UAE
    (wael.salameh@adu.ac.ae)

3  Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid,
    (msbataineh@just.edu.jo)

4  Department of Mathematics, Jerash University, Jerash 26150, Jordan
    (m.alqadri@jpu.edu.jo)

5  Department of Mathematics, College of Science and Art, AlUla branch, Taibah University, Medina, Saudi Arabia
    (aaahmdi@taibahu.edu.sa)

6  Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, Jordan
    (dralhosban@inu.edu.jo)

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Doi   :   https://doi.org/10.54216/IJNS.230431

Received: June 12, 2023 Revised: January 22, 2024 Accepted: March 22, 2024

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; Linear Diophantine equation.

References :

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[8]      Ahmad, K., Bal, M., and Aswad, M.,  A Short Note On The Solutions Of Fermat's Diophantine Equation In Some Neutrosophic Rings, Journal Of Neutrosophic and Fuzzy Systems, (2022).

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[10]   Alfahal, A., Abobala, M., Alhasan, Y., and Abdulfatah, R., Generating Weak Fuzzy Complex and Anti Weak Fuzzy Complex Integer Solutions for Pythagoras Diophantine Equation X2+Y2=Z2, International Journal of Neutrosophic Science, 22, (2023).

[11]   Alhasan, Y., Xu, L., Abdulfatah, R., & Alfahal, A., The Geometrical Characterization for The Solutions of a Vectorial Equation By Using Weak Fuzzy Complex Numbers and Other Generalizations Of Real Numbers. International Journal of Neutrosophic Science (IJNS), 21, (2023), 155-159. https://doi.org/10.54216/IJNS.210415

[12]    Galarza, F., Flores, M., Rivero, D., & Abobala, M., On Weak Fuzzy Complex Pythagoras Quadruples. International Journal of Neutrosophic Science (IJNS), 22, (2023), 108-113. https://doi.org/10.54216/IJNS.220209 .

[13]   Razouk,L., Mahmoud, S., & Ali, M., A Computer Program For The System Of Weak Fuzzy Complex Numbers And Their Arithmetic Operations Using Python. Galoitica: Journal Of Mathematical Structures and Applications, 8, (2023), 45-51. https://doi.org/10.54216/GJMSA.080104.

[14]   Merkepci, M., and Abobala, M., " On Some Novel Results About Split-Complex Numbers, The Diagonalization Problem And Applications To Public Key Asymmetric Cryptography", Journal of Mathematics, Hindawi, 2023.

[15]   Murtada Ali Maqdisi. (2023). The Decay of The Solutions of a Nonlinear Viscoelastic Hyperbolic Equation. Journal of Pure Mathematics for Theoretical Computer Science, 1 ( 1 ), 47-55 (Doi   :  https://doi.org/10.54216/PMTCS.010104)

 

 

Cite this Article as :
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MLA Mayada Abualhomos, Wael Mahmoud M. Salameh, Malik Bataineh, Mowafaq Omar Al-Qadri, Ayman Alahmade, Abdallah Al-Husban. "An Effective Algorithm for Solving Weak Fuzzy Complex Diophantine Equations in Two Variables." International Journal of Neutrosophic Science, Vol. 23, No. 4, 2024 ,PP. 386-394 (Doi   :  https://doi.org/10.54216/IJNS.230431)
APA Mayada Abualhomos, Wael Mahmoud M. Salameh, Malik Bataineh, Mowafaq Omar Al-Qadri, Ayman Alahmade, Abdallah Al-Husban. (2024). An Effective Algorithm for Solving Weak Fuzzy Complex Diophantine Equations in Two Variables. Journal of International Journal of Neutrosophic Science, 23 ( 4 ), 386-394 (Doi   :  https://doi.org/10.54216/IJNS.230431)
Chicago Mayada Abualhomos, Wael Mahmoud M. Salameh, Malik Bataineh, Mowafaq Omar Al-Qadri, Ayman Alahmade, Abdallah Al-Husban. "An Effective Algorithm for Solving Weak Fuzzy Complex Diophantine Equations in Two Variables." Journal of International Journal of Neutrosophic Science, 23 no. 4 (2024): 386-394 (Doi   :  https://doi.org/10.54216/IJNS.230431)
Harvard Mayada Abualhomos, Wael Mahmoud M. Salameh, Malik Bataineh, Mowafaq Omar Al-Qadri, Ayman Alahmade, Abdallah Al-Husban. (2024). An Effective Algorithm for Solving Weak Fuzzy Complex Diophantine Equations in Two Variables. Journal of International Journal of Neutrosophic Science, 23 ( 4 ), 386-394 (Doi   :  https://doi.org/10.54216/IJNS.230431)
Vancouver Mayada Abualhomos, Wael Mahmoud M. Salameh, Malik Bataineh, Mowafaq Omar Al-Qadri, Ayman Alahmade, Abdallah Al-Husban. An Effective Algorithm for Solving Weak Fuzzy Complex Diophantine Equations in Two Variables. Journal of International Journal of Neutrosophic Science, (2024); 23 ( 4 ): 386-394 (Doi   :  https://doi.org/10.54216/IJNS.230431)
IEEE Mayada Abualhomos, Wael Mahmoud M. Salameh, Malik Bataineh, Mowafaq Omar Al-Qadri, Ayman Alahmade, Abdallah Al-Husban, An Effective Algorithm for Solving Weak Fuzzy Complex Diophantine Equations in Two Variables, Journal of International Journal of Neutrosophic Science, Vol. 23 , No. 4 , (2024) : 386-394 (Doi   :  https://doi.org/10.54216/IJNS.230431)
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