(untitled) (European Journal of Pure and Applied Mathematics, 2025)
This paper presents a detailed exploration of Sheffer stroke Hilbert algebras, introducing the innovative concepts of length fuzzy ideals and mean fuzzy ideals within an interval-valued fuzzy framework. These new constructs extend classical ideal theory by incorporating fuzzy logic, providing precise mathematical tools to analyze and measure membership gradations. Specifically, the study establishes critical relationships between length fuzzy ideals and mean fuzzy ideals, their hierarchical subsets, and their implications for algebraic consistency and computational logic. Key findings demonstrate that length fuzzy ideals align closely with interval-valued fuzzy subsets, while mean fuzzy ideals offer a unique averaging perspective for understanding ideal structures. These contributions significantly advance the field of fuzzy algebra, offering theoretical insights and potential applications in computational logic, uncertainty modeling, and algorithmic design.