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Title

On The Foundations of Fuzzy Number Theory and Fuzzy Diophantine Equations

  Mohammad Abobala 1 *

1  Department of Mathematics, Faculty of Sciences, Tishreen University, Syria
    (mohammadabobala777@gmail.com)


Doi   :   https://doi.org/10.54216/GJMSA.0100102

Received: June 20, 2023 Revised: August 25, 2023 Accepted: December 17, 2023

Abstract :

Despite the great and rapid progress in the study of Fuzzy Logic and its applications in various scientific fields, it has not yet been used to build a consistent number theory like classical number theory. This research provides for the first time a conception of the concepts of number theory based on fuzzy logic and fuzzy membership functions, where it defines the division process, the fuzzy congruence, the greatest common divisor between integers with a fuzzy membership function. On the other hand, it presents many famous Diophantine equations formulated using fuzzy sets, in addition to many properties of fuzzy number theoretical systems, through many related theorems and accompanying illustrative examples. Also, in this research, we are raising many open research questions related to fuzzy number theory, which we believe will represent the future of progress in the study of this new mathematical branch.

Keywords :

Fuzzy Number Theory; fuzzy Diophantine equation; standard fuzzy number theoretical system; fuzzy divisor; fuzzy prime; fuzzy gcd.

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Cite this Article as :
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MLA Mohammad Abobala. "On The Foundations of Fuzzy Number Theory and Fuzzy Diophantine Equations." Galoitica: Journal of Mathematical Structures and Applications, Vol. 10, No. 1, 2023 ,PP. 17-25 (Doi   :  https://doi.org/10.54216/GJMSA.0100102)
APA Mohammad Abobala. (2023). On The Foundations of Fuzzy Number Theory and Fuzzy Diophantine Equations. Journal of Galoitica: Journal of Mathematical Structures and Applications, 10 ( 1 ), 17-25 (Doi   :  https://doi.org/10.54216/GJMSA.0100102)
Chicago Mohammad Abobala. "On The Foundations of Fuzzy Number Theory and Fuzzy Diophantine Equations." Journal of Galoitica: Journal of Mathematical Structures and Applications, 10 no. 1 (2023): 17-25 (Doi   :  https://doi.org/10.54216/GJMSA.0100102)
Harvard Mohammad Abobala. (2023). On The Foundations of Fuzzy Number Theory and Fuzzy Diophantine Equations. Journal of Galoitica: Journal of Mathematical Structures and Applications, 10 ( 1 ), 17-25 (Doi   :  https://doi.org/10.54216/GJMSA.0100102)
Vancouver Mohammad Abobala. On The Foundations of Fuzzy Number Theory and Fuzzy Diophantine Equations. Journal of Galoitica: Journal of Mathematical Structures and Applications, (2023); 10 ( 1 ): 17-25 (Doi   :  https://doi.org/10.54216/GJMSA.0100102)
IEEE Mohammad Abobala, On The Foundations of Fuzzy Number Theory and Fuzzy Diophantine Equations, Journal of Galoitica: Journal of Mathematical Structures and Applications, Vol. 10 , No. 1 , (2023) : 17-25 (Doi   :  https://doi.org/10.54216/GJMSA.0100102)