Multilattices on typical hesitant fuzzy sets

In this paper, we mainly study multilattices on the set of finite nonempty subsets of [0,1] under different orders. Firstly, the relationships among orders <=(1), <=(2) and are discussed. It is shown that the order <=* is contained in the orders <= 1 and <=(2), but the converse is not true, and that there is no inclusion between the orders <=(1) and <=(2). The lattice and multilattice structures of the set of finite nonempty subsets of [0,1] under <=(1) and <=* are studied, respectively. It is proved that the set of finite nonempty subsets of [0,1] is neither a lattice nor a multilattice with respect to the order <= and is not a multilattice with respect to the order <=(1). Finally, we extend order <= to the set V(10, 11) of finite vectors of [0,1] and develop a new order <=. It is verified that the quotient set V(10, 1])/ under the order <= is not a lattice, but is a multilattice. Moreover, we give a method to construct maximal elements and minimal elements for finite vectors of [0,1] with respect to the order <= The results will provide an application of hesitant fuzzy sets in rough sets, information fusion, fuzzy automata, fuzzy transitive systems, etc. (C) 2019 Elsevier Inc All rights reserved.