Partial orderings for hesitant fuzzy sets

(H,≤H) is a bounded partially ordered set but not a lattice. Nevertheless, it will be shown that some interesting subsets of (H,≤H) have a lattice structure. Moreover in the set B of finite bags or multisets (i.e. allowing repetition of objects) of the unit interval a preorder ≤B can be defined in a similar way as ≤H in H and considering the quotient set B‾=B/∼ of B by the equivalence relation ∼ defined by A∼B when A≤BB and B≤BA, (B‾,≤B) is a lattice and (H,≤H) can be naturally embedded into it.