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Volume 13
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10.3390/math13172786
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

GE-Algebras Advanced by Intuitionistic Fuzzy Points

by
Amal S. Alali
1,†,
Ravi Kumar Bandaru
2,*,†,
Seok-Zun Song
3,† and
Young Bae Jun
4,†
1
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2
Department of Mathematics, School of Advanced Sciences, VIT-AP University, Andhra Pradesh 522237, India
3
Department of Mathematics, Jeju National University, Jeju 63243, Republic of Korea
4
Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Republic of Korea
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Mathematics 2025, 13(17), 2786; https://doi.org/10.3390/math13172786
Submission received: 1 August 2025 / Revised: 22 August 2025 / Accepted: 28 August 2025 / Published: 29 August 2025
(This article belongs to the Special Issue Algebra and Discrete Mathematics, 4th Edition)
Versions Notes

Abstract

In this paper, we introduce the notion of intuitionistic fuzzy GE-algebra by combining the concepts of GE-algebras and intuitionistic fuzzy sets. We provide a necessary and sufficient condition for an intuitionistic fuzzy set to form an intuitionistic fuzzy GE-algebra. This study examines various properties and characterizations of intuitionistic fuzzy GE-algebra. In particular, we explore the roles of (ℷA,t)∈,(ðA,s)∈,(ℷA,t)q,(ðA,s)q,(ℷA,t)∈∨q, and (ðA,s)∈∨q sets in determining the subalgebra structures within GE-algebras. Examples illustrate the results, and counterexamples clarify the necessity of the conditions. These results not only enhance the theory of GE-algebras, but also contribute to the algebraic treatment of uncertainty using intuitionistic fuzzy logic.
Keywords: GE-algebra; intuitionistic fuzzy GE-algebra; intuitionistic fuzzy point; GE-subalgebra GE-algebra; intuitionistic fuzzy GE-algebra; intuitionistic fuzzy point; GE-subalgebra

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MDPI and ACS Style

Alali, A.S.; Bandaru, R.K.; Song, S.-Z.; Jun, Y.B. GE-Algebras Advanced by Intuitionistic Fuzzy Points. Mathematics 2025, 13, 2786. https://doi.org/10.3390/math13172786

AMA Style

Alali AS, Bandaru RK, Song S-Z, Jun YB. GE-Algebras Advanced by Intuitionistic Fuzzy Points. Mathematics. 2025; 13(17):2786. https://doi.org/10.3390/math13172786

Chicago/Turabian Style

Alali, Amal S., Ravi Kumar Bandaru, Seok-Zun Song, and Young Bae Jun. 2025. "GE-Algebras Advanced by Intuitionistic Fuzzy Points" Mathematics 13, no. 17: 2786. https://doi.org/10.3390/math13172786

APA Style

Alali, A. S., Bandaru, R. K., Song, S.-Z., & Jun, Y. B. (2025). GE-Algebras Advanced by Intuitionistic Fuzzy Points. Mathematics, 13(17), 2786. https://doi.org/10.3390/math13172786

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