In this paper, we utilize the Lukasiewicz t-norm to construct a novel class of fuzzy sets, termed ζ-Lukasiewicz fuzzy sets, derived from a given fuzzy framework. These sets are then applied to the structure of Sheffer stroke BE-algebras (SBE-algebras). We introduce and examine the concepts of ζ-Lukasiewicz fuzzy SBE-subalgebras and ζ-Lukasiewicz fuzzy SBE-ideals, with a focus on their algebraic properties. Furthermore, we define three specific types of subsets, referred to as ∈-sets, q-sets, and O-sets, and investigate the necessary conditions for these subsets to constitute subalgebras or ideals within the SBE-algebraic context.