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GE-Algebras Advanced by Intuitionistic Fuzzy Points

Author

Listed:
  • Amal S. Alali

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
    These authors contributed equally to this work.)

  • Ravi Kumar Bandaru

    (Department of Mathematics, School of Advanced Sciences, VIT-AP University, Amaravati 522237, India
    These authors contributed equally to this work.)

  • Seok-Zun Song

    (Department of Mathematics, Jeju National University, Jeju 63243, Republic of Korea
    These authors contributed equally to this work.)

  • Young Bae Jun

    (Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Republic of Korea
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Amal S. Alali & Ravi Kumar Bandaru & Seok-Zun Song & Young Bae Jun, 2025. "GE-Algebras Advanced by Intuitionistic Fuzzy Points," Mathematics, MDPI, vol. 13(17), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:17:p:2786-:d:1737748
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