Completable fuzzy metric spaces

In the context of fuzzy metrics in the sense of George and Veeramani, we introduce the concept of stratified fuzzy metric. Many well-known fuzzy metrics are stratified. We prove that stratified strong fuzzy metric spaces (X,M,⁎) are completable, under the assumption that ⁎ is integral (positive). In particular, stratified fuzzy ultrametric spaces are completable.