Volume 23 , Issue 4 , PP: 386-394, 2024 | Cite this article as | XML | Html | PDF | Full Length Article
Mayada Abualhomos 1 , Wael Mahmoud M. Salameh 2 * , Malik Bataineh 3 , Mowafaq Omar Al-Qadri 4 , Ayman Alahmade 5 , Abdallah Al-Husban 6
Doi: https://doi.org/10.54216/IJNS.230431
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.
Weak fuzzy complex integer , Diophantine system , Linear Diophantine equation.
[1] Deckelman, S., Robson, B. Split-Complex Numbers and Dirac Bra-kets., Communications In Information and Systems,14, (2014), 135-159.
[2] Akar, M., Yuce, S., Sahin, S., On the Dual Hyperbolic Numbers and The Complex Hyperbolic Numbers, JCSCM, 8, (2018), DOI: 10.20967/jcscm.2018.01.001.
[3] Hatip, A., An Introduction To Weak Fuzzy Complex Numbers, Galoitica Journal Of Mathematical Structures and Applications, 3, (2023).
[4] Ali, R., On The Weak Fuzzy Complex Inner Products On Weak Fuzzy Complex Vector Spaces, Neoma Journal Of Mathematics and Computer Science, (2023).
[5] Hatip, A., On The Weak Fuzzy Complex Vector Spaces, Galoitica Journal Of Mathematical Structures And Applications, 3, (2023).
[6] Ali, R., A Short Note On The Solution of n-Refined Neutrosophic Linear Diophantine Equations, International Journal Of Neutrosophic Science, 15, (2021).
[7] Alhasan,Y., Alfahal, A., Abdulfatah, R., Nordo, G.& Zahra, M., On Some Novel Results About Weak Fuzzy Complex Matrices. International Journal of Neutrosophic Science, 21, (2023), 134-140. https://doi.org/10.54216/IJNS.210112
[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).
[9] Abobala, M., Partial Foundation of Neutrosophic Number Theory, Neutrosophic Sets and Systems, 39 , (2021).
[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)
