GE-Algebras Advanced by Intuitionistic Fuzzy Points

Amal S. Alali, Ravi Kumar Bandaru (), Seok-Zun Song and Young Bae Jun
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Amal S. Alali: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Ravi Kumar Bandaru: Department of Mathematics, School of Advanced Sciences, VIT-AP University, Amaravati 522237, India
Seok-Zun Song: Department of Mathematics, Jeju National University, Jeju 63243, Republic of Korea
Young Bae Jun: Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Republic of Korea

Mathematics, 2025, vol. 13, issue 17, 1-13

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 ( ℷ A , t ) ∈ , ( ð A , s ) ∈ , ( ℷ A , t ) q , ( ð A , s ) q , ( ℷ A , t ) ∈ ∨ q , and ( ð A , 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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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