If all we know about normalized fuzzy sets is which set is a subset of which, will we be able to detect crisp sets? It is known that we can do it if we allow all possible fuzzy sets, including non-normalized ones. In this paper, we show that a similar detection is possible if we only allow normalized fuzzy sets. We also show that we can detect type-1 fuzzy sets based on the subsethood ordering of normalized interval-valued fuzzy sets.