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Title

On the Concepts of Two- Fold Fuzzy Vector Spaces and Algebraic Modules

  Ahmed Hatip 1 * ,   Necati Olgun 2

1  Gaziantep University, Department of Mathematics, Gaziantep, Turkey
    (kollnaar5@gmail.com)

2  Gaziantep University, Department of Mathematics, Gaziantep, Turkey
    (olgun@gantep.edu.tr)

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Doi   :   https://doi.org/10.54216/JNFS.070205

Received: May 22, 2023 Revised: September 19, 2023 Accepted: November 22, 2023

Abstract :

The concept of two-fold algebras is generated by merging some special sets such as fuzzy sets, neutrosophic sets or plithogenic sets with various algebraic structures. The main objective of this research paper is to provide a strict mathematical definition and a general study of two-fold fuzzy vector spaces defined over the real numbers and also two-fold fuzzy vector spaces defined over the complex numbers, as well as two-fold fuzzy algebraic modules defined over commutative rings with unity. The elementary properties and algebraic operations of those structures will be explained through many theorems and mathematical proofs.

Keywords :

two-fold fuzzy algebra , two-fold fuzzy vector space , two-fold fuzzy module

References :

[1] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 ( 1971), 512-517.

[2] P. Sivaramakrishna Das, Fuzzy groups and level subgroups, J. Math. Anal. Appl. 84 (1981), 264- 269.

[3] Mohammad Abobala. (2020). n-Cyclic Refined Neutrosophic Algebraic Systems of Sub-Indeterminacies, An Application to Rings and Modules. International Journal of Neutrosophic Science, 12 ( 2 ), 81-95 (Doi   :  https://doi.org/10.54216/IJNS.120203)

[4] Malath Fared Alaswad, Rasha Dallah. (2023). Neutrosophic Divisor Point of A Straight Line Segment With A Given Ratio. Pure Mathematics for Theoretical Computer Science, 2 ( 1 ), 18-23 (Doi   :  https://doi.org/10.54216/PMTCS.020102)

[5] Mohammad Abobala, Mikail Bal, Ahmed Hatip. (2021). A Review on Recent Advantages in Algebraic Theory of Neutrosophic Matrices. International Journal of Neutrosophic Science, 17 ( 1 ), 68-86 (Doi   :  https://doi.org/10.54216/IJNS.170105)

[6] T. M. Anthony, H. Sherwood, A characterization of fuzzy subgroups, Fuzzy Sets and Systems 7 (1982), 297-305.

[7] W. M.Wu, “Normal fuzzy subgroups,” Fuzzy Mathematics, vol.1, no. 1, pp. 21–30, 1981.

[8] Palaniappan, N, Naganathan,S and Arjunan, K “ A study on Intuitionistic L-Fuzzy Subgroups”, Applied Mathematical Sciences, vol. 3 , 2009, no. 53 , 2619-2624.

[9] Noor Edin Rabeh, Othman Al-Basheer, Sara Sawalmeh, Rozina Ali. (2023). An Algebraic Approach to n-Plithogenic Square Matrices For 18 ≤ n ≤ 19. Journal of Neutrosophic and Fuzzy Systems, 7 ( 2 ), 08-23 (Doi   :  https://doi.org/10.54216/JNFS.070201)

[10] M.A. Ibrahim, A.A.A. Agboola , E.O. Adeleke, S.A. Akinleye. (2020). On Neutrosophic Quadruple Hypervector Spaces. International Journal of Neutrosophic Science, 4 ( 1 ), 20-35 (Doi   :  https://doi.org/10.54216/IJNS.040103)

[11] Mohammad Abobala. (2020). Classical Homomorphisms Between n-Refined Neutrosophic Rings. International Journal of Neutrosophic Science, 7 ( 2 ), 74-78 (Doi   :  https://doi.org/10.54216/IJNS.070204)

[12] Mohammad Abobala. (2020). Classical Homomorphisms Between Refined Neutrosophic Rings and Neutrosophic Rings. International Journal of Neutrosophic Science, 5 ( 2 ), 72-75 (Doi   :  https://doi.org/10.54216/IJNS.050202)

[13] P.K. Sharma , “( α , β ) – Cut of Intuitionistic fuzzy Groups” International Mathematical Forum ,Vol. 6, 2011 , no. 53 , 2605-2614.

[14] Mohammad Abobala, On a Two-Fold Algebra Based on the Standard Fuzzy Number Theoretical System, Journal of Journal of Neutrosophic and Fuzzy Systems, Vol. 7 , No. 2 , (2023) : 24-29 (Doi   :  https://doi.org/10.54216/JNFS.070202)

[15] 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).

[16] Mohammad Abobala. (2023). On a Two-Fold Algebra Based on the Standard Fuzzy Number Theoretical System. Journal of Neutrosophic and Fuzzy Systems, 7 ( 2 ), 24-29 (Doi   :  https://doi.org/10.54216/JNFS.070202)

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MLA Ahmed Hatip, Necati Olgun. "On the Concepts of Two- Fold Fuzzy Vector Spaces and Algebraic Modules." Full Length Article, Vol. 7, No. 2, 2023 ,PP. 46-52 (Doi   :  https://doi.org/10.54216/JNFS.070205)
APA Ahmed Hatip, Necati Olgun. (2023). On the Concepts of Two- Fold Fuzzy Vector Spaces and Algebraic Modules. Journal of Full Length Article, 7 ( 2 ), 46-52 (Doi   :  https://doi.org/10.54216/JNFS.070205)
Chicago Ahmed Hatip, Necati Olgun. "On the Concepts of Two- Fold Fuzzy Vector Spaces and Algebraic Modules." Journal of Full Length Article, 7 no. 2 (2023): 46-52 (Doi   :  https://doi.org/10.54216/JNFS.070205)
Harvard Ahmed Hatip, Necati Olgun. (2023). On the Concepts of Two- Fold Fuzzy Vector Spaces and Algebraic Modules. Journal of Full Length Article, 7 ( 2 ), 46-52 (Doi   :  https://doi.org/10.54216/JNFS.070205)
Vancouver Ahmed Hatip, Necati Olgun. On the Concepts of Two- Fold Fuzzy Vector Spaces and Algebraic Modules. Journal of Full Length Article, (2023); 7 ( 2 ): 46-52 (Doi   :  https://doi.org/10.54216/JNFS.070205)
IEEE Ahmed Hatip, Necati Olgun, On the Concepts of Two- Fold Fuzzy Vector Spaces and Algebraic Modules, Journal of Full Length Article, Vol. 7 , No. 2 , (2023) : 46-52 (Doi   :  https://doi.org/10.54216/JNFS.070205)
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