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.
