This study focuses on developing and analyzing generalized versions of topological IL-algebras. ILalgebras provide the algebraic framework corresponding to a specific fragment of linear logic. These structures generalize various algebras corresponding to t-norm based fuzzy logics. A distinguishing aspect of IL-algebras is that their monoidal unit 1 need not coincide with the lattice’s top element ⊤, unlike conventional fuzzy logic algebras. The monoidal conjunction of an IL-algebra, defined on −1, 2, is an extension of the Lukasiewicz tnorm, a basis in fuzzy set theory. The primary contribution of this work lies in examining weaker variants of topological IL-algebras, namely semi-topological and para-topological IL-algebras, with respect to the principal algebraic operations. Evidently, every topological IL-algebra is also para-topological, and every para-topological ILalgebra is semi-topological; however, the reverse implications are not valid. Compactness, connectedness, and other topological properties are studied in these generalized structures. Moreover, algebraic and topological properties of these weaker algebras are generalizations of the same of the conventional fuzzy logic algebras.
Islam et al. (Wed,) studied this question.