On imaginable \(T\)-fuzzy subalgebras and imaginable \(T\)-fuzzy closed ideals in BCH-algebras (Q5957220)

Summary: We inquire further into the properties on fuzzy closed ideals. We give a characterization of a fuzzy closed ideal using its level set, and establish some conditions for a fuzzy set to be a fuzzy closed ideal. We describe the fuzzy closed ideal generated by a fuzzy set, and give a characterization of a finite-valued fuzzy closed ideal. Using a t-norm \(T\), we introduce the notion of (imaginable) \(T\)-fuzzy subalgebras and (imaginable) \(T\)-fuzzy closed ideals, and obtain some related results. We give relations between an imaginable \(T\)-fuzzy subalgebra and an imaginable \(T\)-fuzzy closed ideal. We discuss the direct product and \(T\)-product of \(T\)-fuzzy subalgebras. We show that the family of \(T\)-fuzzy closed ideals is a completely distributive lattice.