Weak Filters of Sheffer Stroke Hilbert Algebras Based on the Intuitionistic Fuzzy Set

Abstract

Using the concept of intuitionistic fuzzy points, the weak filter in Sheffer stroke Hilbert algebras is addressed. The notion of intuitionistic fuzzy weak filters in Sheffer stroke Hilbert algebras is introduced, and their properties are investigated. Conditions under which the intuitionistic fuzzy set becomes an intuitionistic fuzzy weak filter are examined. Characterizations of intuitionistic fuzzy weak filters are considered, and conditions under which the intuitionistic fuzzy set becomes an intuitionistic fuzzy weak filter are discussed. The (0, 1)-set for the intuitionistic fuzzy set is established, and the phases in which it can be a weak filter are explored. Conditions for an intuitionistic level set and an intuitionistic q-set to be weak filters are provided. © 2025 Elsevier B.V., All rights reserved.