Lattice embeddings between types of fuzzy sets. Closed-valued fuzzy sets
  In this paper we deal with the problem of extending Zadeh's operators on
fuzzy sets (FSs) to interval-valued (IVFSs), set-valued (SVFSs) and type-2
(T2FSs) fuzzy sets. Namely, it is known that seeing FSs as SVFSs, or T2FSs,
whose membership degrees are singletons is not order-preserving. We then
describe a family of lattice embeddings from FSs to SVFSs. Alternatively, if
the former singleton viewpoint is required, we reformulate the intersection on
hesitant fuzzy sets and introduce what we have called closed-valued fuzzy sets.
This new type of fuzzy sets extends standard union and intersection on FSs. In
addition, it allows handling together membership degrees of different nature
as, for instance, closed intervals and finite sets. Finally, all these
constructions are viewed as T2FSs forming a chain of lattices.
