Structural Analysis of Intuitionistic Fuzzy Implicative WSBG-Ideals

Authors

  • Tahsin Oner Department of Mathematics, Faculty of Science, Ege University, 35100 Izmir, Turkey
  • Aiyared Iampan Department of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand https://orcid.org/0000-0002-0475-3320
  • Neelamegarajan Rajesh Department of Mathematics, Rajah Serfoji Government College, Thanjavur-613005, Tamil Nadu, India
  • Ibrahim Senturk Department of Mathematics, Faculty of Science, Ege University, 35100 Izmir, Turkey

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.5894

Keywords:

Sheffer stroke (BG-algebra), Intuitionistic fuzzy SBG-subalgebras, Intuitionistic fuzzy SBG-ideals

Abstract

In this paper, we investigate intuitionistic fuzzy WSBG-ideals and intuitionistic fuzzy implicative WSBG-ideals within the framework of Sheffer stroke BG-algebras. We establish new algebraic structures that extend classical Boolean and BG-algebra frameworks by synthesizing intuitionistic fuzzy set theory, introduced by Atanassov, with the Sheffer stroke operation. We demonstrate a fundamental connection between intuitionistic fuzzy implicative WSBG-ideals and their level sets, showing that the level set of an intuitionistic fuzzy implicative WSBG-ideal corresponds to an implicative WSBG-ideal of the Sheffer stroke BG-algebra. Furthermore, we explore the properties of intuitionistic fuzzy WSBG-ideals, proving that every intuitionistic fuzzy implicative WSBG-ideal is also an intuitionistic fuzzy WSBG-ideal. However, the converse does not always hold. This work provides new insights into the algebraic properties of Sheffer stroke BG-algebras, enabling novel reasoning methods under uncertainty and paving the way for further applications in fuzzy logic and computational models.

Downloads

Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Algebra

License

Copyright (c) 2025 Tahsin Oner, Aiyared Iampan, Neelamegarajan Rajesh, Ibrahim Senturk

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

Structural Analysis of Intuitionistic Fuzzy Implicative WSBG-Ideals. (2025). European Journal of Pure and Applied Mathematics, 18(3), 5894. https://doi.org/10.29020/nybg.ejpam.v18i3.5894