On interval-valued intuitionistic fuzzy subalgebras of Sheffer stroke Hilbert algebras

Abstract

This paper explores the structure of interval-valued intuitionistic fuzzy (IVIF) subsets within the framework of Sheffer stroke Hilbert algebras (SSHAs). After establishing the foundational definitions of interval-valued intuitionistic fuzzy Sheffer stroke subalgebras (IVIFSSsubalgebras), we investigate their algebraic properties, closure under Sheffer stroke operations, and stability under set-theoretic intersections and unions. A key result characterizes IVIFSSsubalgebras through a pair of membership conditions, and it is further shown that the level subsets corresponding to IVIF-degrees form classical subalgebras in the crisp setting. These findings demonstrate that IVIF extensions preserve core algebraic behaviors while offering a robust model for uncertainty. The results contribute to the ongoing generalization of fuzzy algebraic systems and lay the groundwork for further developments involving fuzzy ideals and logical applications.