On Interval-Valued Intuitionistic Fuzzy Subalgebras of Sheffer Stroke Hilbert Algebras
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i4.7074Keywords:
Sheffer stroke Hilbert algebra, intuitionistic fuzzy set, interval-valued intuitionistic fuzzy subalgebraAbstract
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 (IVIFSS-subalgebras), we investigate their algebraic properties, closure under Sheffer stroke operations, and stability under set-theoretic intersections and unions. A key result characterizes IVIFSS-subalgebras 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.
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Copyright (c) 2025 Aiyared Iampan, Neelamegarajan Rajesh, Tahsin Oner, Tahsin Oner, Firat Ates, Kannan Geetha, Arsham Borumand Saeid
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