Author’s abstract: In this paper [a follow up to Part I, J. Math. Anal. Appl. 262, 473-489 (2001; Zbl 0989.54006)], we study relations induced by fuzzy closure operators (fuzzy quasiorders and similarities); factorization of closure systems by similarities and by so-called decrease of logical precision; representation of fuzzy closure operators by (crisp) closure operators; relation to consequence relations; and natural examples illustrating the notions and results.