Q-Fuzzy JU-Algebras: A Structural Analysis with Respect to ⊗

K.  Perarasan; M.  Vasuki; Anjay Kumar Mishra; B. Mohamed  Harif; A. Dinesh  Kumar; Mbonigaba  Celestin

Authors

K. Perarasan Annai Vailankanni Arts and Science College (Affiliated to Bharathidasan University), Thanjavur, Tamil Nadu, India
M. Vasuki Srinivasan College of Arts and Science (Affiliated to Bharathidasan University), Perambalur, Tamil Nadu, India
Anjay Kumar Mishra Dean, Madhesh University, Birgunj, Nepal http://orcid.org/0000-0003-2803-4918
B. Mohamed Harif Government Arts College (Affiliated to Bharathidasan University), Tiruchirappalli, Tamil Nadu, India
A. Dinesh Kumar Khadir Mohideen College (Affiliated to Bharathidasan University), Adirampattinam, Tamil Nadu, India
Mbonigaba Celestin Brainae Institute of Professional Studies, Brainae University, Delaware, United States of America

Keywords:

JU-algebra, Q-fuzzy set, Cartesian product, Intersection

Abstract

This paper introduces fuzzy algebras, a new type of algebraic structure. We explore their basic properties, showing how these "fuzzy" structures behave like their regular counterparts. Key findings include how these fuzzy algebras combine through intersections and Cartesian products, and how they transform under homomorphisms. We also define fuzzy ideals, a special kind of fuzzy sub algebra, and show their relationship to fuzzy subalgebras. This work lays the groundwork for understanding and applying these new fuzzy algebraic concepts.

How to cite this article:

K Perarasan, M. Vasuki, Mishra A.K, B. Mohamed Harif, A. Dinesh Kumar, Celestin M, Q Fuzzy JU-Algebras: A Structural Analysis with Respect to ⊗, J Adv Res Appl Math Stat, Vol 11, Issue 1&2 2026: Pg. No. 39-49.

DOI: https://doi.org/10.24321/2455.7021.202607

Author Biography

Anjay Kumar Mishra, Dean, Madhesh University, Birgunj, Nepal

Post Doctoral Research Scholar, Srinivas University, India and Associate Professor, Madan Bhandari Memorial Academy Nepal, Urlabari 3, Morang, Nepal.

References

Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353.

Rosenfeld, A. (1971). Fuzzy groups. Journal of mathematical analysis and applications, 35(3), 512-517.

B. C. R. (1988). Fuzzy ideals in BCK-algebras. Math. Japonica, 33(3), 475-478.

Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy sets and systems, 20(1), 87-96.

Reeves, D. A., & Ahmad, I. (2024). Q-fuzzy ideals in KU-algebras. Journal of Intelligent & Fuzzy Systems, 46(1), 1-10.

Al-Ghamdi, H. A., & Al-Amri, S. S. (2023). On (α, β)-fuzzy (∈, ∈∨qk)-ideals of BCI-algebras. Journal of Discrete Mathematical Sciences and Cryptography, 26(8), 2419-2428.

Zulkifli, S., & Bidin, S. (2022). Q-Fuzzy Ideals and Q-Fuzzy Filters in MV-algebras.AIP Conference Proceedings, 2592(1), 020008.

Ali, S. M., & Khan, S. S. (2021). Q-fuzzy ideals of semirings.International Journal of Mathematics Trends and Technology, 67(1), 1-8.

Naeem, R. (2021). On Q-fuzzy KU-ideals of KU-algebras.Journal of Physics: Conference Series, 1856(1), 012028.

Abdullah, S. F., & Hamzah, W. N. W. (2020). Q-fuzzy filter and Q-fuzzy ideal on BL-algebras.Malaysian Journal of Fundamental and Applied Sciences, 16(1), 163-169.

Al-Musawa, M. H., & Al-Saadi, W. A. (2020). On Q-fuzzy ideals in BCK/BCI-algebras.Journal of College of Education for Pure Sciences, 10(4), 167-175.

Ma, Y., Ding, Y., & Li, R. (2020). Some New Results on Q-fuzzy Ideals in G-algebras.Journal of Mathematics, 2020.

Ullah, A., & Ahmad, S. (2020). Q-fuzzy filters in lattice implication algebras.Journal of Algebra and Related Topics, 8(2), 51-64

Yadav, B., & Kumar, S. (2024). A study on Q-fuzzy rough ideals in ordered semigroups.Discrete Mathematics, Algorithms and Applications, 16(01), 2450002.