Generalized Fuzzy Subalgebras of Sheffer Stroke Hilbert Algebras

Authors

  • Neelamegarajan Rajesh Rajah Serfoji Government College
  • Aiyared Iampan Department of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand https://orcid.org/0000-0002-0475-3320
  • Tahsin Oner Ege University
  • Arsham Borumand Saeid Shahid Bahonar University of Kerman

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6500

Keywords:

Sheffer stroke Hilbert algebra, subalgebra, fuzzy set, fuzzy subalgebra

Abstract

This paper introduces new generalized fuzzy subalgebras and investigates their important properties within the framework of Sheffer stroke Hilbert algebras. We characterize these generalized subalgebras through their level subsets and establish key properties that define their structure. The Sheffer stroke operation, known for its ability to construct logical systems independently of other operators, plays a central role in our study. Using fuzzy set theory, we adapt the traditional ideas of subalgebras to fit fuzzy contexts, giving a detailed look at $(\in, \in \vee q_m)$-fuzzy subalgebras. Our results include necessary and sufficient conditions for a fuzzy set to qualify as such a subalgebra, along with theorems addressing their intersections, unions, and homomorphic invariance. This work contributes to the broader understanding of algebraic structures in fuzzy logic and their applications in logical systems.

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Published

2025-08-02

Issue

Vol. 18 No. 3: (July 2025)

Section

Algebra

License

Copyright (c) 2025 Neelamegarajan Rajesh, Aiyared Iampan, Tahsin Oner, Arsham Borumand Saeid

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How to Cite

Generalized Fuzzy Subalgebras of Sheffer Stroke Hilbert Algebras. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6500. https://doi.org/10.29020/nybg.ejpam.v18i3.6500