Generalized Fuzzy Subalgebras of Sheffer Stroke Hilbert Algebras (European Journal of Pure and Applied Mathematics, 2025)
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.