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Journal of Discrete Mathematical Sciences and Cryptography cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

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Open Access Research Article

New structure of bipolar fuzzy rho-ideals in rho-algebraic semigroups 

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pp. 1145–1151Vol. 28Issue 4-AJune 2025DOI: 10.47974/JDMSC-2120 Crossmark XML
Received:
11 Dec 2024
Published Online:
26 Jun 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2120
Pages:
1145–1151

Abstract

In algebraic semigroups when we deal with classical sets every ρ-ideal does not have to be ρ–-ideal. As a result, it is demonstrated in this study with their expansion in some kinds of sets as fuzzy set (FS) & bipolar fuzzy set (BFS) is held. Also, a new construction of (BFS) is demonstrated in ρ-algebras. The study of novel notions such as ρ-semigroup (ρ-SG), ρ-subsemigroup (ρ-SSG), ρ–-ideal semigroup (ρ–-ISG), ρ-ideal semigroup (ρ-ISG), and other are given. Moreover, their extensions in fuzzy logic (FL) using Bipolar fuzzy are introduced. Additionally, a number of basic characteristics of our concepts are investigated and explored. 

Keywords

Subject Classifications

Primary 06F35Secondary 03G25

References

[1] L. A. Zadeh, “Fuzzy Sets,” Information and Control, vol. 8, pp. 338–353 (1965).
[2] P. Maji, A. Roy, and R. Biswas, “Fuzzy soft sets,” Journal of Fuzzy Mathematics, vol. 9, no. 3, pp. 589–602 (2001).
[3] S. Mahmood, “Decision Making Using New Category of Similarity Measures and Study Their Applications in Medical Diagnosis Problems,” Afrika Matematika, vol. 32, pp. 865–878 (2021). DOI: 10.1007/s13370-020-00866-2.
[4] A. A. Atshan and S. Khalil, “On fuzzy normal RHO-filters and usual RHO-filters of RHO-algebras,” AIP Conference Proceedings, vol. 2834, no. 1, pp. 080036 (2023).
[5] S. Mahmood and A. Hassan, “Applications of Fuzzy Soft ρ-Ideals in ρ-Algebras,” Fuzzy Information and Engineering, vol. 10, no. 4, pp. 467–475 (2018).
[6] S. Bashir, R. Mazhar, H. Abbas, and M. Shabir, “Regular ternary semirings in terms of bipolar fuzzy ideals,” Computational and Applied Mathematics, vol. 39, no. 4, pp. 1–18 (2020).
[7] Y. B. Jun, H. S. Kim, and K. J. Lee, “Bipolar fuzzy translation in BCK/BCI-algebra,” Journal of the Chungcheong Mathematical Society, vol. 22, no. 3, pp. 399–408 (2009).
[8] G. Muhiuddin, “Bipolar Fuzzy KU-Subalgebras/Ideals of KU-Algebras,” Annals of Fuzzy Mathematics and Informatics, vol. 8, no. 3, pp. 409–418 (2014).
[9] S. Khalil and F. Hameed, “Applications of Fuzzy ρ-Ideals in ρ-Algebras,” Soft Computing, vol. 24, pp. 13997–14004 (2020).
[10] K. M. Lee, “Bipolar-Valued Fuzzy Sets and Their Operations,” in Proceedings of International Conference on Intelligent Technologies, Bangkok, Thailand, pp. 307–312 (2000).
[11] T. Meghwar, S. Khan Awan, M. Tariq, M. Suleman, and A. A. Shaikh, “Substitutional Based Gauss-Seidel Method for Solving System of Linear Algebraic Equations,” Babylonian Journal of Mathematics, pp. 1–12 (2024).
[12] S. H. Asaad, I. S. Ahmed, and A. S. Mohammed, “Generalization Fuzzy Completely Intra G-ideals in G-Semi Groups,” Journal of Physics: Conference Series, vol. 1664, no. 1 (2020). DOI: 10.1088/1742-6596/1664/1/012028.

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