Abstract: Dual hesitant fuzzy sets (DHFSs), originally introduced by Zhu et al. [23], are a new tool to handle fuzziness considering the membership and nonmembership degrees by a set of possible values respectively. As a more comprehensive set, DHFSs have close relationship with the existing fuzzy sets, including the Zadeh's fuzzy set, Atanassov's intuitionistic fuzzy set, and hesitant fuzzy set, etc. And under certain conditions, DHFSs can also reduce to some existing fuzzy sets. However, sometimes the related operations of DHFSs do not have uniform expressions by considering different conditions. To better understand DHFSs, distinguish them from other fuzzy sets, and make further research of DHFSs, in this paper we develop typical DHFSs (T-DHFSs), and present a good number of operations and properties, which shall provide the good theory foundation of DHFSs.
