Volume 7 • Issue 2 • PP: 24-29 • 2023
On a Two-Fold Algebra Based on the Standard Fuzzy Number Theoretical System
Open Access & Copyright
© 2023 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
View PDF Abstract
This paper is dedicated to studying the algebraic structure generated from the fusion of two-fold algebras with the standard fuzzy number theoretical system, where the novel fuzzy algebraic structure will be defined with a well-defined binary operation, and then its substructures will be studied concerning the corresponding operation such as hyper/under ideals, and two-fold fuzzy homomorphisms. Also, many examples will be illustrated to clarify the validity of our work.
Keywords
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] T. M. Anthony, H. Sherwood, A characterization of fuzzy subgroups, Fuzzy Sets and Systems 7 (1982), 297-305.
[4] W. M.Wu, “Normal fuzzy subgroups,” Fuzzy Mathematics, vol.1, no. 1, pp. 21–30, 1981.
[5] Palaniappan, N, Naganathan,S and Arjunan, K “ A study on Intuitionistic L-Fuzzy Subgroups”, Applied Mathematical Sciences, vol. 3 , 2009, no. 53 , 2619-2624.
[6] P.K. Sharma , “( α , β ) – Cut of Intuitionistic fuzzy Groups” International Mathematical Forum ,Vol. 6, 2011 , no. 53 , 2605-2614.
[7] Florentine Smarandache. "Neutrosophic Two-Fold Algebra", Plithogenic Logic and Computation, Vol.1, No.1 2024. PP.11-15.
[8] 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).
Cite This Article
Choose your preferred format
Publisher's Note
The statements, opinions, and data presented in this article are solely those of the author(s) and do not necessarily represent those of ASPG, the journal, or its editors. ASPG and the editors disclaim responsibility for any harm arising from the use of any ideas, methods, instructions, or products described in this article, to the fullest extent permitted by applicable law.